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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 11051. |
A steel rod 100 cm long is clamped at its mid-point. The funda-mental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel [AFMC 2000] |
| A. | 5.06 km/s |
| B. | 6.06 km/s |
| C. | 7.06 km/s |
| D. | 8.06 km/s |
| Answer» B. 6.06 km/s | |
| 11052. |
Which of the following is the example of transverse wave [CPMT 1999] |
| A. | Sound waves |
| B. | Compressional waves in a spring |
| C. | Vibration of string |
| D. | All of these |
| Answer» D. All of these | |
| 11053. |
A stretched string of 1m length and mass \[5\times {{10}^{-4}}kg\] is having tension of 20N. If it is plucked at 25cm from one end then it will vibrate with frequency [RPET 1999; RPMT 2002] |
| A. | 100 Hz |
| B. | 200 Hz |
| C. | 256 Hz |
| D. | 400 Hz |
| Answer» C. 256 Hz | |
| 11054. |
Two similar sonometer wires given fundamental frequencies of 500Hz. These have same tensions. By what amount the tension be increased in one wire so that the two wires produce 5 beats/sec [RPET 1999] |
| A. | 0.01 |
| B. | 0.02 |
| C. | 0.03 |
| D. | 0.04 |
| Answer» C. 0.03 | |
| 11055. |
The equation of stationary wave along a stretched string is given by \[y=5\sin \frac{\pi x}{3}\cos 40\pi t\], where x and y are in cm and t in second. The separation between two adjacent nodes is [CPMT 1990; MP PET 1999; AMU 1999; DPMT 2004; BHU 2005] |
| A. | 1.5 cm |
| B. | 3 cm |
| C. | 6 cm |
| D. | 4 cm |
| Answer» C. 6 cm | |
| 11056. |
For the stationary wave \[y=4\sin \,\left( \frac{\pi x}{15} \right)\cos (96\,\pi t)\], the distance between a node and the next antinode is[MP PMT 1987] |
| A. | 7.5 |
| B. | 15 |
| C. | 22.5 |
| D. | 30 |
| Answer» B. 15 | |
| 11057. |
Stationary waves are formed when [NCERT 1983] |
| A. | Two waves of equal amplitude and equal frequency travel along the same path in opposite directions |
| B. | Two waves of equal wavelength and equal amplitude travel along the same path with equal speeds in opposite directions |
| C. | Two waves of equal wavelength and equal phase travel along the same path with equal speed |
| D. | Two waves of equal amplitude and equal speed travel along the same path in opposite direction |
| Answer» C. Two waves of equal wavelength and equal phase travel along the same path with equal speed | |
| 11058. |
A string vibrates according to the equation \[y=5\sin \,\left( \frac{2\pi x}{3} \right)\,\,\cos \,20\,\pi t\], where x and y are in cm and t in sec. The distance between two adjacent nodes is [UPSEAT 2005] |
| A. | 3 cm |
| B. | 4.5 cm |
| C. | 6 cm |
| D. | 1.5 cm |
| Answer» E. | |
| 11059. |
Two travelling waves \[{{y}_{1}}=A\sin [k(x-c\,t)]\] and \[{{y}_{2}}=A\sin [k(x+c\,t)]\] are superimposed on string. The distance between adjacent nodes is [IIT 1992] |
| A. | \[c\,t/\pi \] |
| B. | \[c\,t/2\pi \] |
| C. | \[\pi /2k\] |
| D. | \[\pi /k\] |
| Answer» E. | |
| 11060. |
The following equations represent progressive transverse waves \[{{Z}_{1}}=A\cos (\omega \,t-kx)\], \[{{Z}_{2}}=A\cos (\omega \,t+kx)\], \[{{Z}_{3}}=A\cos (\omega \,t+ky)\] and \[{{Z}_{4}}=A\cos (2\omega \,t-2ky)\]. A stationary wave will be formed by superposing [MP PET 1993] |
| A. | \[{{Z}_{1}}\] and \[{{Z}_{2}}\] |
| B. | \[{{Z}_{1}}\] and \[{{Z}_{4}}\] |
| C. | \[{{Z}_{2}}\] and \[{{Z}_{3}}\] |
| D. | \[{{Z}_{3}}\] and \[{{Z}_{4}}\] |
| Answer» B. \[{{Z}_{1}}\] and \[{{Z}_{4}}\] | |
| 11061. |
Equation of a stationary wave is \[y=10\sin \frac{\pi x}{4}\cos 20\pi t.\] Distance between two consecutive nodes is [MP PMT 2002] |
| A. | 4 |
| B. | 2 |
| C. | 1 |
| D. | 8 |
| Answer» B. 2 | |
| 11062. |
In stationary waves [RPMT 1998; JIPMER 2002] |
| A. | Energy is uniformly distributed |
| B. | Energy is minimum at nodes and maximum at antinodes |
| C. | Energy is maximum at nodes and minimum at antinodes |
| D. | Alternating maximum and minimum energy producing at nodes and antinodes |
| Answer» C. Energy is maximum at nodes and minimum at antinodes | |
| 11063. |
When a stationary wave is formed then its frequency is [Kerala (Engg.) 2002] |
| A. | Same as that of the individual waves |
| B. | Twice that of the individual waves |
| C. | Half that of the individual waves |
| D. | None of the above |
| Answer» B. Twice that of the individual waves | |
| 11064. |
The stationary wave produced on a string is represented by the equation\[y=5\cos (\pi x/3)\sin 40\pi t\]. Where x and y are in cm and \[t\] is in seconds. The distance between consecutive nodes is [MP PMT 2000] |
| A. | 5 cm |
| B. | \[\pi \] cm |
| C. | 3 cm |
| D. | 40 cm |
| Answer» D. 40 cm | |
| 11065. |
Energy is not carried by which of the following waves [RPMT 1998; AIIMS 1998, 99] |
| A. | Stationary |
| B. | Progressive |
| C. | Transverse |
| D. | Electromagnetic |
| Answer» B. Progressive | |
| 11066. |
Two waves are approaching each other with a velocity of 20 m/s and frequency\[n\]. The distance between two consecutive nodes is [Pb. PMT 1999] |
| A. | \[\frac{20}{n}\] |
| B. | \[\frac{10}{n}\] |
| C. | \[\frac{5}{n}\] |
| D. | \[\frac{n}{10}\] |
| Answer» C. \[\frac{5}{n}\] | |
| 11067. |
A standing wave is represented by \[Y=A\sin (100t)\cos (0.01x)\] where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of wave is [CBSE PMT 1994; AFMC 2002] |
| A. | \[{{10}^{4}}\,m/s\] |
| B. | \[1\,m/s\] |
| C. | \[{{10}^{-4}}\,m/s\] |
| D. | Not derivable from above data |
| Answer» B. \[1\,m/s\] | |
| 11068. |
Which two of the given transverse waves will give stationary waves when get superimposed [RPET 1997; MP PET 1993] \[{{z}_{1}}=a\cos (kx-\omega \,t)\] ..... \[{{z}_{2}}=a\cos (kx+\omega \,t)\] ..... \[{{z}_{3}}=a\cos (ky-\omega \,t)\] ..... |
| A. | A and B |
| B. | A and C |
| C. | B and C |
| D. | Any two |
| Answer» B. A and C | |
| 11069. |
Stationary waves of frequency 300 Hz are formed in a medium in which the velocity of sound is 1200 metre/sec. The distance between a node and the neighbouring antinode is [SCRA 1994] |
| A. | 1 m |
| B. | 2 m |
| C. | 3 m |
| D. | 4 m |
| Answer» B. 2 m | |
| 11070. |
In stationary wave [MP PET 1987; BHU 1995] |
| A. | Strain is maximum at nodes |
| B. | Strain is maximum at antinodes |
| C. | Strain is minimum at nodes |
| D. | Amplitude is zero at all the points |
| Answer» D. Amplitude is zero at all the points | |
| 11071. |
The distance between the nearest node and antinode in a stationary wave is [MP PET 1984; CBSE PMT 1993; AFMC 1996; RPET 2002] |
| A. | l |
| B. | \[\frac{\lambda }{2}\] |
| C. | \[\frac{\lambda }{4}\] |
| D. | 2l |
| Answer» D. 2l | |
| 11072. |
A speeding motorcyclist sees trafic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speeds of sound is 343 m/s, the frequency of the honk as heard by him will be : |
| A. | 1332 Hz |
| B. | 1372 Hz |
| C. | 1412Hz |
| D. | 1464Hz |
| Answer» D. 1464Hz | |
| 11073. |
A police car moving at 22 m/s, chases a motorcyclist. The policeman sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. The speed of the motorcycle, if it is given that he does not observe any beats is |
| A. | 33 m/s |
| B. | 22 m/s |
| C. | zero |
| D. | 11 m/s |
| Answer» C. zero | |
| 11074. |
Two sources of sound placed close to each other are emitting progressive waves given by\[{{y}_{1}}=4\sin 600\pi t\] and\[{{y}_{2}}=5\sin 608\pi t\]. An observer located near these two sources of sound will hear: |
| A. | 4 beats per second with intensity ratio 25 : 16 between waxing and waning. |
| B. | 8 beats per second with intensity ratio 25 : 16 between waxing and waning |
| C. | 8 beats per second with intensity ratio 81: 1 between waxing and waning |
| D. | 4 beats per second with intensity ratio 81 : 1 between waxing and waning |
| Answer» E. | |
| 11075. |
In a transverse wave the distance between a crest and neighboring trough at the same instant is 4.0 cm and the distance between a crest and trough at the same place is 1.0 cm. The next crest appears at the same place after a time interval of 0.4s.The maximum speed of the vibrating particles in the medium is: |
| A. | \[\frac{3\pi }{2}cm/s\] |
| B. | \[\frac{5\pi }{2}cm/s\] |
| C. | \[\frac{\pi }{2}cm/s\] |
| D. | \[2\pi cm/s\] |
| Answer» C. \[\frac{\pi }{2}cm/s\] | |
| 11076. |
The extension in a string, obeying Hooke's law, is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5x, the speed of sound will be |
| A. | 1.22v |
| B. | 0.61v |
| C. | 1.50v |
| D. | 0.75v |
| Answer» B. 0.61v | |
| 11077. |
The amplitude of a wave disturbance propagating in the positive x-direction is given by \[y=\frac{1}{1+{{x}^{2}}}\] at t=0 and \[y=\frac{1}{2+{{x}^{2}}-2x}\] at t = 2s, where x and y are in meter. Assuming that the shape of the wave disturbance does not change during the propagation, the speed of the wave is |
| A. | \[0.5m/s\] |
| B. | \[~1m/s\] |
| C. | \[1.5m/s\] |
| D. | \[2\text{ }m/s\] |
| Answer» B. \[~1m/s\] | |
| 11078. |
A transverse wave is represented by\[y=A\sin (\omega t+kx)\]. For what value of the wavelength is the wave velocity equal to the maximum particle velocity? |
| A. | \[\frac{\pi A}{2}\] |
| B. | \[\pi A\] |
| C. | \[2\pi A\] |
| D. | \[A\] |
| Answer» D. \[A\] | |
| 11079. |
On earth, a body suspended on a spring of negligible mass causes extension L and undergoes oscillations along length of the spring with frequency f. On the Moon, the same quantities are L/n and f respectively. The ratio f?/f is |
| A. | n |
| B. | \[\frac{1}{n}\] |
| C. | \[{{n}^{-1/2}}\] |
| D. | 1 |
| Answer» E. | |
| 11080. |
A particle at the end of a spring executes S.H.M with a period\[{{t}_{1}}\], while the corresponding period for another spring is \[{{t}_{2}}\]. If the period of oscillation with the two springs in series is T then |
| A. | \[{{T}^{-1}}={{t}_{1}}^{-1}+{{t}_{2}}^{-1}\] |
| B. | \[{{T}^{2}}=t_{1}^{2}+t_{2}^{2}\] |
| C. | \[T={{t}_{1}}+{{t}_{2}}\] |
| D. | \[{{T}^{-2}}=t_{1}^{-2}+t_{2}^{-2}\] |
| Answer» C. \[T={{t}_{1}}+{{t}_{2}}\] | |
| 11081. |
A particle executes simple harmonic motion between \[x=-A\] and \[x=+A\]. The time taken for it to go from O to A/2 is \[{{T}_{1}}\] and\[{{T}_{1}}\] and to go from A/2 to A is \[{{T}_{2}}\]. Then |
| A. | \[{{T}_{1}}<{{T}_{2}}\] |
| B. | \[{{T}_{1}}>{{T}_{2}}\] |
| C. | \[{{T}_{1}}={{T}_{2}}\] |
| D. | \[{{T}_{1}}=2{{T}_{2}}\] |
| Answer» B. \[{{T}_{1}}>{{T}_{2}}\] | |
| 11082. |
A particle of mass 10 gm is describing S.H. M. along a straight line with period of 2 sec and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is |
| A. | \[37.5{{\pi }^{2}}\,ergs\] |
| B. | \[3.75{{\pi }^{2}}\,ergs\] |
| C. | \[375{{\pi }^{2}}\,ergs\] |
| D. | \[0.375{{\pi }^{2}}\,erg\] |
| Answer» D. \[0.375{{\pi }^{2}}\,erg\] | |
| 11083. |
If< E > and < U> denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is |
| A. | <E>=<U> |
| B. | <E>=2<U> |
| C. | <E>=-2<U> |
| D. | <E>=-< U> |
| Answer» B. <E>=2<U> | |
| 11084. |
Two simple harmonic motions of angular frequency 100 and 1000 r\[rad\,{{s}^{-1}}\]have the same displacement amplitude. The ratio of their maximum accelerations is: |
| A. | 0.0486111111111111 |
| B. | \[1:{{10}^{2}}\] |
| C. | \[1:{{10}^{3}}\] |
| D. | \[1:{{10}^{4}}\] |
| Answer» C. \[1:{{10}^{3}}\] | |
| 11085. |
Part of a simple harmonic motion is graphed in the figure, where y is the displacement from the mean position. The correct equation describing this S.H. M. is |
| A. | \[y=4\cos (0.6t)\] |
| B. | \[y=2\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] |
| C. | \[y=4\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] |
| D. | \[y=2\cos \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] |
| Answer» C. \[y=4\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] | |
| 11086. |
A particle starts with S.H.M. from the mean position as shown in figure below. Its amplitude is A and its time period is T. At one time, its speed is half that of the maximum speed. What is the displacement at that time? |
| A. | \[\frac{\sqrt{2}A}{3}\] |
| B. | \[\frac{\sqrt{3}A}{2}\] |
| C. | \[\frac{2A}{\sqrt{3}}\] |
| D. | \[\frac{3A}{\sqrt{2}}\] |
| Answer» C. \[\frac{2A}{\sqrt{3}}\] | |
| 11087. |
The displacement vs time of a particle executing SHM is shown in figure. The initial phase \[\phi \] is |
| A. | \[-\pi <\phi <-\frac{\pi }{2}\] |
| B. | \[\pi <\phi <\frac{3\pi }{2}\] |
| C. | \[-\frac{3\pi }{2}<\phi <-\pi \] |
| D. | \[\frac{\pi }{2}<\phi <\pi \] |
| Answer» B. \[\pi <\phi <\frac{3\pi }{2}\] | |
| 11088. |
A particle of mass 1 kg is moving in S.H.M. with an amplitude 0.02 and a frequency of 60 Hz. The maximum force acting on is |
| A. | 144\[{{\pi }^{2}}\] |
| B. | 188 \[{{\pi }^{2}}\] |
| C. | 288\[{{\pi }^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 11089. |
For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is |
| A. | \[3:\pi \] |
| B. | \[\pi :3\] |
| C. | \[1:\pi \] |
| D. | \[\pi :1\] |
| Answer» B. \[\pi :3\] | |
| 11090. |
A wire suspended vertically from one of its ends is stretched by attaching a weight of 200N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is |
| A. | 0.2 J |
| B. | 10 J |
| C. | 20 J |
| D. | 0.1 J |
| Answer» E. | |
| 11091. |
The pressure in an explosion chamber is 345 MPa. What would be the percent change in volume of a piece of copper subjected to this pressure? The bulk modulus for copper is 138 \[Gpa\]\[(=138\times {{10}^{9}}Pa)\] |
| A. | 0.001 |
| B. | 0.005 |
| C. | 0.0025 |
| D. | 0.002 |
| Answer» D. 0.002 | |
| 11092. |
When the load on a wire is increasing slowly from 2 kg to 4 kg, the elongation increases from 0.6 mm to 1 mm. The work done during this extension of the wire is (\[g=10m/{{s}^{2}}\]) |
| A. | \[9\times {{10}^{-3}}J\] |
| B. | \[12\times {{10}^{-3}}J\] |
| C. | \[14\times {{10}^{-3}}J\] |
| D. | \[16\times {{10}^{-3}}J\] |
| Answer» D. \[16\times {{10}^{-3}}J\] | |
| 11093. |
A material has poisson?s ratio 0.50. If a uniform rod of it suffers a longitudinal strain of \[2\times {{10}^{-3}}\], then the percentage change in volume is |
| A. | 0.6 |
| B. | 0.4 |
| C. | 2 |
| D. | Zero |
| Answer» C. 2 | |
| 11094. |
A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is |
| A. | 0.01 |
| B. | 0.06 |
| C. | 0.02 |
| D. | 0.03 |
| Answer» E. | |
| 11095. |
The ratio of shearing stress to the corresponding shearing strain is called |
| A. | Bulk modulus |
| B. | Young's modulus |
| C. | Modulus of rigidity |
| D. | None of these |
| Answer» D. None of these | |
| 11096. |
A metal wire of length \[{{L}_{1}}\]and area of cross-section A is attached to a rigid support. Another metal wire of length \[{{L}_{2}}\] and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If \[{{Y}_{1}}\]and \[{{Y}_{2}}\] are the young's moduli of the wires respectively, the effective force constant of the system of two wires is |
| A. | \[\frac{({{Y}_{1}}{{Y}_{2}})A}{2({{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}})}\] |
| B. | \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{({{L}_{1}}{{L}_{2}})}^{1/2}}}\] |
| C. | \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}}}\] |
| D. | \[\frac{{{({{Y}_{1}}{{Y}_{2}})}^{1/2}}A}{{{({{L}_{2}}{{L}_{1}})}^{1/2}}}\] |
| Answer» D. \[\frac{{{({{Y}_{1}}{{Y}_{2}})}^{1/2}}A}{{{({{L}_{2}}{{L}_{1}})}^{1/2}}}\] | |
| 11097. |
A steel wire of length / and cross section area A is stretched by 1 cm under a given load. When the same load is applied to another steel wire of double its length and half of its cross section area, the amount of stretching (extension) is |
| A. | 0.5 cm |
| B. | 2cm |
| C. | 4cm |
| D. | 1.5cm |
| Answer» D. 1.5cm | |
| 11098. |
One end of uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight \[{{W}_{1}}\] is suspended from its lower end. Ifs is the area of cross section of the wire, the stress in the wire at a height\[\left( \frac{3L}{4} \right)\] from its lower end is |
| A. | \[\frac{{{W}_{1}}}{s}\] |
| B. | \[\left[ {{W}_{1}}+\frac{W}{4} \right]s\] |
| C. | \[\left[ {{W}_{1}}+\frac{3W}{4} \right]/s\] |
| D. | \[\frac{{{W}_{1}}+W}{s}\] |
| Answer» D. \[\frac{{{W}_{1}}+W}{s}\] | |
| 11099. |
Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is |
| A. | Four times for wire A as for wire B |
| B. | Twice for wire A as for wire B |
| C. | Half for wire A as for wire B |
| D. | One-fourth for wire A as for wire B |
| Answer» E. | |
| 11100. |
If the equation of transverse wave is \[Y=2\sin (kx-2t),\] then the maximum particle velocity is [Orissa JEE 2005] |
| A. | 4 units |
| B. | 2 units |
| C. | 0 |
| D. | 6 units |
| Answer» B. 2 units | |