A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by:

\({\rm{\;}}2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\left( {{\rm{g}} + \frac{{{\rm{qE}}}}{{\rm{m}}}} \right)}}} \)

\({\rm{\;}}2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\sqrt {{{\rm{g}}^2} - \frac{{{{\rm{q}}^2}{{\rm{E}}^2}}}{{{{\rm{m}}^2}}}} }}} \)

\(2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\left( {{\rm{g}} - \frac{{{\rm{qE}}}}{{\rm{m}}}} \right)}}} \)

\(2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\sqrt {{{\rm{g}}^2} + {{\left( {\frac{{{\rm{qE}}}}{{\rm{m}}}} \right)}^2}} }}} \)

A simple pendulum is made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. Then, M is given by

\(\frac{{\rm{m}}}{2}\left( {\frac{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}} \right)\)

\({\rm{m}}\left( {\frac{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}} \right)\)

\(\frac{{\rm{m}}}{2}\left( {\frac{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}} \right)\)

\({\rm{m}}\left( {\frac{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}} \right)\)

\(\frac{{\rm{m}}}{2}\left( {\frac{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}} \right)\)

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T, so that its momentum changes from p to 3p. Here, k is a constant. The value of T is

\({\rm{\;}}\sqrt {\frac{{2k}}{p}}\)

\({\rm{\;}}2\sqrt {\frac{p}{k}} \)

\({\rm{\;}}\sqrt {\frac{{2k}}{p}}\)

\({\rm{\;}}2\sqrt {\frac{k}{p}}\)

If a clock loses 5 seconds per day, what is the alteration required in the length of the pendulum in order that the clock keeps correct time?

\(\frac{4}{{8640}}\) times its original length be shortened

\(\frac{4}{{86400}}\) times its original length be shortened

\(\frac{1}{{86400}}\) times its original length be shortened

\(\frac{1}{{8640}}\) times its original length be shortened

\(\frac{4}{{8640}}\) times its original length be shortened

If 'V' is the magnitude of velocity, 'A' is the magnitude of acceleration and 'X' is the magnitude of displacement, then at the mean position of the particle performing simple harmonic motion, __________.

V and A are maximum and X is zero

A is maximum and X and V are zero

V is maximum and X and A are zero

V and A are maximum and X is zero

X and A are maximum and V is zero

A pendulum oscillates 30 times in 3 seconds. Choose the correct statement from among the following:

It's time period is 10 s and frequency is 0.3 Hz.

It's time period is 10 s and frequency 3Hz.

It's time period is 0.1 s and frequency is 10 Hz.

It's time period is 10 s and frequency is 0.3 Hz.

It's time period is 0.3 s and frequency is 0.3 Hz.

A particle of mass m is moving along a trajectory given byx = x0 + a cos ω1ty = y0 + b sin ω2tThe torque, acting on the particle about the origin, at t = 0 is:

\(m\left( { - {x_0}b + {y_0}a} \right)\omega _1^2\hat k\)

\( + m{y_0}a\omega _1^2\hat k\)

\( - m\left( {{x_0}b\omega _2^2 - {y_0}a\omega _1^2} \right)\hat k\)

In simple harmonic motion the acceleration is proportional to

Rate of change of angular velocity

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude θ0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l (l

\(Mgl\left( {1 - \theta _0^2} \right)\)

\(Mgl\left( {1 + \theta _0^2} \right)\)

\(Mgl\left( {1 + \frac{{\theta _0^2}}{2}} \right)\)

A smooth wire of length 2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2 is equal to:

\(\frac{{{\rm{g}}\sqrt 3 }}{{\rm{r}}}\)

\(\frac{{\sqrt 3 {\rm{g}}}}{{2{\rm{r}}}}\)

\(\frac{{2{\rm{g}}}}{{{\rm{r}}\sqrt 3 }}\)

\(\frac{{{\rm{g}}\sqrt 3 }}{{\rm{r}}}\)

\(\frac{{2{\rm{g}}}}{{\rm{r}}}\)

A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?

It is maximum when the speed is maximum

It is always in the opposite direction to the velocity

It is proportional to the frequency of oscillation

It is maximum when the speed is maximum

It decreases as potential energy increases

A particle executes linear simple harmonic motion with an amplitude of 2 cm. when the particle is at 1 cm from the mean position, the magnitude of the velocity and the acceleration are equal. Then its item period (in seconds) is

\(\frac{{2\pi }}{{\sqrt 3 }}\;\)

If 'V' is magnitude of velocity, 'A' is magnitude of acceleration and 'X' is magnitude of displacement, then at the extreme position of the particle performing simple harmonic motion, ___________________.

V is maximum and X and A are zero.

X and A are maximum and V is zero.

V is maximum and X and A are zero.

A is maximum and X and V are zero.

V and A are maximum and X is zero.

92 + Mcqs in Oscillations in BITSAT Page 1 McqOptions

1.	A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:
A.	666 Hz
B.	753 Hz
C.	500 Hz
D.	333 Hz
Answer» B. 753 Hz

Discussion

2.	If the argument 'ωt' of the periodic function f(t) = A cos(ωt + φ) is increased by integral multiple of ______ radians, the value of the function remainsthe same.
A.	π
B.	2φ
C.	φ
D.	2π
Answer» E.

Discussion

3.	A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by:
A.	\({\rm{\;}}2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\left( {{\rm{g}} + \frac{{{\rm{qE}}}}{{\rm{m}}}} \right)}}} \)
B.	\({\rm{\;}}2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\sqrt {{{\rm{g}}^2} - \frac{{{{\rm{q}}^2}{{\rm{E}}^2}}}{{{{\rm{m}}^2}}}} }}} \)
C.	\(2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\left( {{\rm{g}} - \frac{{{\rm{qE}}}}{{\rm{m}}}} \right)}}} \)
D.	\(2{\rm{\pi }}\sqrt {\frac{{\rm{L}}}{{\sqrt {{{\rm{g}}^2} + {{\left( {\frac{{{\rm{qE}}}}{{\rm{m}}}} \right)}^2}} }}} \)
Answer» E.

Discussion

4.	Oscillation of a particles is prescribed by the equation x = 3cos (0.25 πt), where is the time in seconds. The time taken by the particle to move from position of equilibrium to maximum displacement is
A.	2.0 sec
B.	1.0 sec
C.	0.5 sec
D.	3.0 sec
Answer» B. 1.0 sec

Discussion

5.	A pendulum clock be taken from the earth to a revolving artificial satellite, it will:
A.	run slow
B.	run fast
C.	given the same time
D.	stop altogether
Answer» E.

Discussion

6.	If 'x' is the displacement of a particle performing simple harmonic motion, then "kx2/2" is equal to its ______________ energy.
A.	kinetic
B.	potential
C.	total mechanical
D.	vibrational
Answer» C. total mechanical

Discussion

7.	A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency mark near the open end of the tube. The 512 Hz e produces first resonance when the tube is filled with water to a mark 11 cm below a reference experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment is close to
A.	328 ms-1
B.	341 ms-1
C.	322 ms-1
D.	335 ms-1
Answer» B. 341 ms-1

Discussion

8.	______________ motion is the projection of uniform circular motion on a diameter of the circle in which the latter motion takes place.
A.	Simple harmonic
B.	Translatory
C.	Rotary
D.	Linear
Answer» B. Translatory

Discussion

9.	In the simple harmonic motion x = √2 sin(ωt – π/4), the phase constant can be shown as?
A.	√2
B.	2π /ω
C.	ωt
D.	7π /4
Answer» E.

Discussion

10.	A simple pendulum is made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. Then, M is given by
A.	\({\rm{m}}\left( {\frac{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}} \right)\)
B.	\(\frac{{\rm{m}}}{2}\left( {\frac{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}} \right)\)
C.	\({\rm{m}}\left( {\frac{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}} \right)\)
D.	\(\frac{{\rm{m}}}{2}\left( {\frac{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}} \right)\)
Answer» B. \(\frac{{\rm{m}}}{2}\left( {\frac{{{{\rm{\theta }}_0} - {{\rm{\theta }}_1}}}{{{{\rm{\theta }}_0} + {{\rm{\theta }}_1}}}} \right)\)

Discussion

11.	A piece of stone tied to a string is made to revolve in a circular orbit of radius r with other end of the string as the centre. If the string breaks, the stone will :
A.	Move away from the centre
B.	Move towards the centre
C.	Move along a tangent
D.	stop
Answer» D. stop

Discussion

12.	A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T, so that its momentum changes from p to 3p. Here, k is a constant. The value of T is
A.	\(\sqrt {\frac{{2p}}{k}}\)
B.	\({\rm{\;}}2\sqrt {\frac{p}{k}} \)
C.	\({\rm{\;}}\sqrt {\frac{{2k}}{p}}\)
D.	\({\rm{\;}}2\sqrt {\frac{k}{p}}\)
Answer» C. \({\rm{\;}}\sqrt {\frac{{2k}}{p}}\)

Discussion

13.	If a clock loses 5 seconds per day, what is the alteration required in the length of the pendulum in order that the clock keeps correct time?
A.	\(\frac{4}{{86400}}\) times its original length be shortened
B.	\(\frac{1}{{86400}}\) times its original length be shortened
C.	\(\frac{1}{{8640}}\) times its original length be shortened
D.	\(\frac{4}{{8640}}\) times its original length be shortened
Answer» D. \(\frac{4}{{8640}}\) times its original length be shortened

Discussion

14.	If 'V' is the magnitude of velocity, 'A' is the magnitude of acceleration and 'X' is the magnitude of displacement, then at the mean position of the particle performing simple harmonic motion, __________.
A.	A is maximum and X and V are zero
B.	V is maximum and X and A are zero
C.	V and A are maximum and X is zero
D.	X and A are maximum and V is zero
Answer» C. V and A are maximum and X is zero

Discussion

15.	A particle is undergoing simple harmonic motion with a period of 2 seconds and amplitude of 2 meters. Its maximum speed in ms-1 is
A.	4 π
B.	2 π
C.	π/2
D.	π
Answer» C. π/2

Discussion

16.	A pendulum oscillates 30 times in 3 seconds. Choose the correct statement from among the following:
A.	It's time period is 10 s and frequency 3Hz.
B.	It's time period is 0.1 s and frequency is 10 Hz.
C.	It's time period is 10 s and frequency is 0.3 Hz.
D.	It's time period is 0.3 s and frequency is 0.3 Hz.
Answer» C. It's time period is 10 s and frequency is 0.3 Hz.

Discussion

17.	A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is
A.	\(\frac{{4\pi }}{3}\)
B.	\(\frac{{8\pi }}{3}\)
C.	\(\frac{{7\pi }}{3}\)
D.	\(\frac{{3\pi }}{8}\)
Answer» C. \(\frac{{7\pi }}{3}\)

Discussion

18.	If the energy of an oscillating particle is continuously dissipated, then oscillations are experiencing ___________.
A.	resonance
B.	beats
C.	damping
D.	harmonic
Answer» D. harmonic

Discussion

19.	A thin strip 10 cm long is on a U-shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm-1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 Ω and air drag negligible, N will be close to:
A.	1000
B.	50000
C.	5000
D.	10000
Answer» D. 10000

Discussion

20.	If 'F' is the force acting on a particle of mass 'm' performing simple harmonic motion, then the time period of the simple harmonic motion is equal to ___________.
A.	2π √(k /m)
B.	2π √(m/k)
C.	1/(2π) x √( m/k)
D.	1/(2π) x √(k/m)
Answer» C. 1/(2π) x √( m/k)

Discussion

21.	A particle of mass m is moving along a trajectory given byx = x0 + a cos ω1ty = y0 + b sin ω2tThe torque, acting on the particle about the origin, at t = 0 is:
A.	\(m\left( { - {x_0}b + {y_0}a} \right)\omega _1^2\hat k\)
B.	\( + m{y_0}a\omega _1^2\hat k\)
C.	Zero
D.	\( - m\left( {{x_0}b\omega _2^2 - {y_0}a\omega _1^2} \right)\hat k\)
Answer» C. Zero

Discussion

22.	For a pendulum of string length 'L', bob of mass 'm', moment of inertia 'I' and the string makes an angle 'θ' with the vertical then the angular acceleration 'α', for the pendulum is given by _________________.
A.	α = (L mg sinθ)/I
B.	α = (–L mg sin2θ )/I
C.	α = (L mg sin2θ)/I
D.	α = (–L mg sinθ)/I
Answer» E.

Discussion

23.	In simple harmonic motion, the particle acceleration lags behind the displacement by a phase angle of __________.
A.	π/2
B.	0
C.	π
D.	2π
Answer» D. 2π

Discussion

24.	A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y = 0.3 sin (0.157x) cos (200πt). The length of the string is:(All quantities are in SI units.)
A.	20 m
B.	80 m
C.	40 m
D.	60 m
Answer» C. 40 m

Discussion

25.	A particle is reciprocating simple harmonic motion (SHM) with an amplitude of 0.003 m and frequency of 20 Hz. The maximum acceleration of the particle attained during the motion is:
A.	57.3 m/s2
B.	50.3 m/s2
C.	55.3 m/s2
D.	47.3 m/s2
Answer» E.

Discussion

26.	If simple harmonic motion is represented by x = A cos(ωt + φ), then 'ω' is _____________.
A.	Displacement
B.	Amplitude
C.	Angular frequency
D.	Phase constant
Answer» D. Phase constant

Discussion

27.	A pendulum clock is lifted to a height where the gravitational acceleration has a certain value g. Another pendulum clock of same length but of double the mass of the bob is lifted to another height where the gravitational acceleration is g/2. The time period of the second pendulum would be:(in terms of period T of the first pendulum)
A.	√2 T
B.	\(\frac{1}{{\surd 2}}T\)
C.	2√2 T
D.	T
Answer» B. \(\frac{1}{{\surd 2}}T\)

Discussion

28.	In simple harmonic motion the acceleration is proportional to
A.	Displacement
B.	Linear velocity
C.	Angular velocity
D.	Rate of change of angular velocity
Answer» B. Linear velocity

Discussion

29.	A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is \(\left( {\frac{1}{{16}}} \right)\)th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:
A.	\(2T\sqrt {\frac{1}{{10}}} \)
B.	\(2T\sqrt {\frac{1}{{14}}} \)
C.	\(4T\sqrt {\frac{1}{{15}}} \)
D.	\(4T\sqrt {\frac{1}{{14}}} \)
Answer» D. \(4T\sqrt {\frac{1}{{14}}} \)

Discussion

30.	A body of mass m that is undergoing simple harmonic motion passes through its equilibrium position, its velocity is
A.	zero
B.	maximum
C.	half of its maximum value
D.	none of the above
Answer» C. half of its maximum value

Discussion

31.	A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude θ0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l (l << L), is close to:
A.	\(Mgl\left( {1 - \theta _0^2} \right)\)
B.	\(Mgl\left( {1 + \theta _0^2} \right)\)
C.	Mgl
D.	\(Mgl\left( {1 + \frac{{\theta _0^2}}{2}} \right)\)
Answer» C. Mgl

Discussion

32.	A smooth wire of length 2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2 is equal to:
A.	\(\frac{{\sqrt 3 {\rm{g}}}}{{2{\rm{r}}}}\)
B.	\(\frac{{2{\rm{g}}}}{{{\rm{r}}\sqrt 3 }}\)
C.	\(\frac{{{\rm{g}}\sqrt 3 }}{{\rm{r}}}\)
D.	\(\frac{{2{\rm{g}}}}{{\rm{r}}}\)
Answer» C. \(\frac{{{\rm{g}}\sqrt 3 }}{{\rm{r}}}\)

Discussion

33.	A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?
A.	It is always in the opposite direction to the velocity
B.	It is proportional to the frequency of oscillation
C.	It is maximum when the speed is maximum
D.	It decreases as potential energy increases
Answer» C. It is maximum when the speed is maximum

Discussion

34.	A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of ‘m’ are attached at distance ‘L/2’ from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to:
A.	0.77
B.	0.57
C.	0.37
D.	0.17
Answer» D. 0.17

Discussion

35.	A particle executes linear simple harmonic motion with an amplitude of 2 cm. when the particle is at 1 cm from the mean position, the magnitude of the velocity and the acceleration are equal. Then its item period (in seconds) is
A.	\(\frac{{2\pi }}{{\sqrt 3 }}\;\)
B.	\(\frac{{\sqrt 3 }}{{2\pi }}\)
C.	\(\frac{{\sqrt 3 }}{\pi }\)
D.	\(\frac{1}{{2\pi \sqrt 3 }}\)
Answer» B. \(\frac{{\sqrt 3 }}{{2\pi }}\)

Discussion

36.	In a piezoelectric generator, the quartz crystal is made to oscillate at its natural frequency of L.C circuit to produce ultrasonic waves of 1 MHz with a capacitor of the capacitance of 25 nF in the tank circuit. Then, the inductance of the coil used in the tank circuit is nearly:
A.	3 μH
B.	2 μH
C.	1 μH
D.	4 μH
Answer» D. 4 μH

Discussion

37.	If 'A' is the maximum displacement of a particle performing simple harmonic motion, then 'kA2/2' is equal to its ______________ energy.
A.	two times of potential
B.	half of kinetic
C.	vibrational
D.	total mechanical
Answer» E.

Discussion

38.	If 'V' is magnitude of velocity, 'A' is magnitude of acceleration and 'X' is magnitude of displacement, then at the extreme position of the particle performing simple harmonic motion, ___________________.
A.	X and A are maximum and V is zero.
B.	V is maximum and X and A are zero.
C.	A is maximum and X and V are zero.
D.	V and A are maximum and X is zero.
Answer» B. V is maximum and X and A are zero.

Discussion

39.	For a simple pendulum the graph between L & T will be-
A.	Hyperbola
B.	Parabola
C.	Straight line
D.	Curved line
Answer» C. Straight line

Discussion

40.	f(t) = sin(4ωt + π/4) has a period equal to?
A.	π/(2ω)
B.	π/ω
C.	2π/ω
D.	(π/4)ω
Answer» B. π/ω

Discussion

41.	If 'F' is the force acting on a particle of mass 'm' performing simple harmonic motion, then in the equation "F = –kx", k is equal to ___________.
A.	m / ω2
B.	mω2
C.	ω√m
D.	m√ω
Answer» C. ω√m

Discussion

42.	A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio B1/B2 is best given by:
A.	1.8
B.	0.7
C.	3.6
D.	2.2
Answer» C. 3.6

Discussion

43.	A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10-2 m. The relative change in the angular frequency of the pendulum is best given by
A.	1 rad/s
B.	10-5 rad/s
C.	10-3 rad/s
D.	10-1 rad/s
Answer» D. 10-1 rad/s

Discussion

44.	A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l1 = 30 cm and l2 = 70 cm. Then, v is equal to:
A.	332 m/s
B.	384 m/s
C.	338 m/s
D.	379 m/s
Answer» C. 338 m/s

Discussion

45.	A pendulum oscillates 60 times in 8 seconds. Its time period is:
A.	1.35 s
B.	0.23 s
C.	2.14 s
D.	0.13 s
Answer» E.

Discussion

46.	An object executes simple harmonic motion with amplitude A. Its acceleration will be maximum when the displacement is
A.	A/4
B.	0
C.	A/2
D.	A
Answer» E.

Discussion

47.	A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then
A.	Th = 0.5 Tc
B.	Th = Tc
C.	Th = 2Tc
D.	Th = 1.5 Tc
Answer» C. Th = 2Tc

Discussion

48.	If simple harmonic motion is represented by x = A cos(ωt + φ), then the maximum and minimum values of this function are ______________.
A.	± ω
B.	± A
C.	± φ
D.	± t
Answer» C. ± φ

Discussion

49.	If simple harmonic motion is represented by x = A cos(ωt + φ), then 'φ' is _____________.
A.	Angular frequency
B.	Displacement
C.	Amplitude
D.	Phase constant
Answer» E.

Discussion

50.	A body of mass 1 kg falls freely from a height of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms-2, the value of x will be close to
A.	8 cm
B.	4 cm
C.	40 cm
D.	80 cm
Answer» B. 4 cm

Discussion

Explore topic-wise MCQs in BITSAT.

A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:

If the argument 'ωt' of the periodic function f(t) = A cos(ωt + φ) is increased by integral multiple of ______ radians, the value of the function remainsthe same.

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by:

Oscillation of a particles is prescribed by the equation x = 3cos (0.25 πt), where is the time in seconds. The time taken by the particle to move from position of equilibrium to maximum displacement is

A pendulum clock be taken from the earth to a revolving artificial satellite, it will:

If 'x' is the displacement of a particle performing simple harmonic motion, then "kx2/2" is equal to its ______________ energy.

______________ motion is the projection of uniform circular motion on a diameter of the circle in which the latter motion takes place.

In the simple harmonic motion x = √2 sin(ωt – π/4), the phase constant can be shown as?

A simple pendulum is made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. Then, M is given by

A piece of stone tied to a string is made to revolve in a circular orbit of radius r with other end of the string as the centre. If the string breaks, the stone will :

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T, so that its momentum changes from p to 3p. Here, k is a constant. The value of T is

If a clock loses 5 seconds per day, what is the alteration required in the length of the pendulum in order that the clock keeps correct time?

If 'V' is the magnitude of velocity, 'A' is the magnitude of acceleration and 'X' is the magnitude of displacement, then at the mean position of the particle performing simple harmonic motion, __________.

A particle is undergoing simple harmonic motion with a period of 2 seconds and amplitude of 2 meters. Its maximum speed in ms-1 is

A pendulum oscillates 30 times in 3 seconds. Choose the correct statement from among the following:

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is

If the energy of an oscillating particle is continuously dissipated, then oscillations are experiencing ___________.

If 'F' is the force acting on a particle of mass 'm' performing simple harmonic motion, then the time period of the simple harmonic motion is equal to ___________.

A particle of mass m is moving along a trajectory given byx = x0 + a cos ω1ty = y0 + b sin ω2tThe torque, acting on the particle about the origin, at t = 0 is:

For a pendulum of string length 'L', bob of mass 'm', moment of inertia 'I' and the string makes an angle 'θ' with the vertical then the angular acceleration 'α', for the pendulum is given by _________________.

In simple harmonic motion, the particle acceleration lags behind the displacement by a phase angle of __________.

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y = 0.3 sin (0.157x) cos (200πt). The length of the string is:(All quantities are in SI units.)

A particle is reciprocating simple harmonic motion (SHM) with an amplitude of 0.003 m and frequency of 20 Hz. The maximum acceleration of the particle attained during the motion is:

If simple harmonic motion is represented by x = A cos(ωt + φ), then 'ω' is _____________.

In simple harmonic motion the acceleration is proportional to

A body of mass m that is undergoing simple harmonic motion passes through its equilibrium position, its velocity is

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude θ0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l (l << L), is close to:

A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?

A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of ‘m’ are attached at distance ‘L/2’ from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to:

A particle executes linear simple harmonic motion with an amplitude of 2 cm. when the particle is at 1 cm from the mean position, the magnitude of the velocity and the acceleration are equal. Then its item period (in seconds) is

In a piezoelectric generator, the quartz crystal is made to oscillate at its natural frequency of L.C circuit to produce ultrasonic waves of 1 MHz with a capacitor of the capacitance of 25 nF in the tank circuit. Then, the inductance of the coil used in the tank circuit is nearly:

If 'A' is the maximum displacement of a particle performing simple harmonic motion, then 'kA2/2' is equal to its ______________ energy.

If 'V' is magnitude of velocity, 'A' is magnitude of acceleration and 'X' is magnitude of displacement, then at the extreme position of the particle performing simple harmonic motion, ___________________.

For a simple pendulum the graph between L & T will be-

f(t) = sin(4ωt + π/4) has a period equal to?

If 'F' is the force acting on a particle of mass 'm' performing simple harmonic motion, then in the equation "F = –kx", k is equal to ___________.

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio B1/B2 is best given by:

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10-2 m. The relative change in the angular frequency of the pendulum is best given by

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l1 = 30 cm and l2 = 70 cm. Then, v is equal to:

A pendulum oscillates 60 times in 8 seconds. Its time period is:

An object executes simple harmonic motion with amplitude A. Its acceleration will be maximum when the displacement is

If simple harmonic motion is represented by x = A cos(ωt + φ), then the maximum and minimum values of this function are ______________.

If simple harmonic motion is represented by x = A cos(ωt + φ), then 'φ' is _____________.

A body of mass 1 kg falls freely from a height of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms-2, the value of x will be close to