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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.
| 5001. |
A person is standing at a distance \[D\] from an isotropic point source of sound. He walks 50.0 m towards the source and observes that the intensity of the sound has doubled. His initial distance \[D\] from the source is |
| A. | \[50\sqrt{2}m\] |
| B. | \[\frac{50\sqrt{2}}{\sqrt{2}-1}m\] |
| C. | \[\frac{50}{\sqrt{2}-1}m\] |
| D. | \[100\sqrt{2}m\] |
| Answer» C. \[\frac{50}{\sqrt{2}-1}m\] | |
| 5002. |
The equation of a wave on a string of linear mass density 0.04 kg/m is given by\[y=0.02(m)sin\left[ 2\pi \left( \frac{t}{0.04(s)}-\frac{x}{0.50(m)} \right) \right]\] The tension in the string is |
| A. | 4.0 N |
| B. | 12.5 N |
| C. | 0.5 N |
| D. | 6.25 N |
| Answer» E. | |
| 5003. |
A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was |
| A. | 256 + 5 Hz |
| B. | 256 + 2 Hz |
| C. | 256 - 2 Hz |
| D. | 256 - 5 Hz |
| Answer» E. | |
| 5004. |
A tuning fork produces 4 beats per second with another fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats per second. The unknown frequency is |
| A. | 286 cps |
| B. | 284 cps |
| C. | 292 cps |
| D. | 290 cps |
| Answer» D. 290 cps | |
| 5005. |
The equations of a travelling and stationary waves are \[{{y}_{1}}=a\sin (\omega t-kx)\] and\[{{y}_{2}}=a\sin \,kx\,cos\,\omega t\]. The phase differences between two points \[{{x}_{1}}=\frac{\pi }{4k\,}\,and\,{{x}_{2}}=\frac{4\pi }{3k}\] are \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\] respectively for two waves, where k is the wave number. The ratio of \[{{\phi }_{1}}/{{\phi }_{2}}\] is |
| A. | 6/7 |
| B. | 44271 |
| C. | 12/13 |
| D. | 44543 |
| Answer» D. 44543 | |
| 5006. |
In sports meet the timing of a 200 m straight dash is recorded at the finish point by starting an accurate stop watch on hearing the sound of starting gun fired at the starting point. The time recorded will be more accurate |
| A. | In winter |
| B. | In summer |
| C. | In all seasons |
| D. | None of these |
| Answer» C. In all seasons | |
| 5007. |
The linear density of a vibrating string is\[{{10}^{-4}}kg/m\]. A transverse wave is propagating on the string, which is described by the equation\[y=0.02\sin (x+30t)\], where \[x\] and\[y\] are in metres and time \[t\] in seconds. Then tension in the string is |
| A. | 0.09 N |
| B. | 0.36 N |
| C. | 0.9 N |
| D. | 3.6 N |
| Answer» B. 0.36 N | |
| 5008. |
A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibration simultaneously in their fundamental mode. The length of the open organ pipe is now halved and of the closed organ pipe is doubled; the number of beats produced will be |
| A. | 8 |
| B. | 7 |
| C. | 4 |
| D. | 2 |
| Answer» C. 4 | |
| 5009. |
Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension in one of them, the beat frequency remains unchanged. Denoting by \[{{T}_{1}}\], \[{{T}_{2}}\], the higher and the lower initial tensions in the strings, then it could be said that while making the above change in tension |
| A. | \[{{T}_{2}}\] was decreased |
| B. | \[{{T}_{2}}\]was increased |
| C. | \[{{T}_{1}}\] was increased |
| D. | \[{{T}_{1}}\]was kept constant |
| Answer» C. \[{{T}_{1}}\] was increased | |
| 5010. |
In Young's double-slit experiment, the slits are illuminated by monochromatic light. The entire set-up is immersed in pure water. Which of the following act cannot restore the original fringe width? |
| A. | Bringing the slits close together. |
| B. | Moving the screen away from the slit plane. |
| C. | Replacing the incident light by that of longer wavelength. |
| D. | Introducing a thin transparent slab in front of one of the slits. |
| Answer» E. | |
| 5011. |
In a double-slit experiment, instead of taking slits of equal width, one slit is made twice as wide as the other. Then in the interference pattern |
| A. | The intensities of both the maxima and the minima increase |
| B. | The intensity of the maxima increases and the minima has zero intensity |
| C. | The intensity of the maxima decreases and that of the minima increases |
| D. | The intensity of the maxima decreases and the minima has zero intensity |
| Answer» B. The intensity of the maxima increases and the minima has zero intensity | |
| 5012. |
In the adjacent diagram, CP represents a wave front and AO and BP, the corresponding two rays. Find the condition on \[\theta \] for constructive interference at P between the ray BP and reflected ray OP |
| A. | \[\cos \theta =3\lambda /2d\] |
| B. | \[\cos \theta =\lambda /4d\] |
| C. | \[\sec \theta -\cos \theta =\lambda /d\] |
| D. | \[\sec \theta -\cos \theta =4\lambda /d\] |
| Answer» C. \[\sec \theta -\cos \theta =\lambda /d\] | |
| 5013. |
Two beams of light having intensities \[I\] and 4\[I\] interfere to produce a fringe pattern on a screen. The phase between the beams is \[\pi /2\] at point A and \[\pi \] at point B. Then, the difference between the resultant intensities at A and B is |
| A. | \[2I\] |
| B. | \[4I\] |
| C. | \[5I\] |
| D. | \[7I\] |
| Answer» C. \[5I\] | |
| 5014. |
In the Young's double slit experiment, if the phase difference between the two waves interfering at a point is\[\phi \], the intensity at that point can be expressed by the expression |
| A. | \[I=\sqrt{{{A}^{2}}+{{B}^{2}}{{\cos }^{2}}\varphi }\] |
| B. | \[I=\frac{A}{B}\cos \varphi \] |
| C. | \[I=A+B\cos \frac{\varphi }{2}\] |
| D. | \[I=A+B\cos \] |
| Answer» E. | |
| 5015. |
In a YDSE light of wavelength\[\lambda =5000\]\[\overset{\text{o}}{\mathop{\text{A}}}\,\]is used which emerges in phase from two slits a distance \[d=3\times {{10}^{-7}}m\] apart. A transparent sheet of thickness\[t=1.5\times {{10}^{-7}}m\], is refractive index n = 1.17, is placed over one of the slits. Where does the central maxima of the interference now appear? |
| A. | \[\frac{D(\mu -1)t}{2d}\] |
| B. | \[\frac{2D(\mu -1)t}{d}\] |
| C. | \[\frac{D(\mu +1)t}{d}\] |
| D. | \[\frac{D(\mu -1)t}{d}\] |
| Answer» E. | |
| 5016. |
A single slit of width a is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern is measured as y. When half of the slit width is covered and illuminated by yellow light of wavelength 600 nm, the width of the diffraction pattern is |
| A. | The pattern vanishes and the width is zero |
| B. | \[y/3\] |
| C. | 3y |
| D. | None of these |
| Answer» D. None of these | |
| 5017. |
In a YDSE bichromatic lights of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1 m. The minimum distance between two successive regions of complete darkness is |
| A. | 4 mm |
| B. | 5.6 mm |
| C. | 14 mm |
| D. | 28 mm |
| Answer» E. | |
| 5018. |
Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is |
| A. | \[1\mu m\] |
| B. | \[30\mu m\] |
| C. | \[100\mu m\] |
| D. | \[300\mu m\] |
| Answer» C. \[100\mu m\] | |
| 5019. |
In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If \[{{I}_{m}}\] be the maximum intensity, the resultant intensity \[I\] when they interfere at phase difference \[\phi \] is given by |
| A. | \[\frac{{{I}_{m}}}{9}(4+5cos\phi )\] |
| B. | \[\frac{{{I}_{m}}}{3}\left( 1+2co{{s}^{2}}\frac{\phi }{2} \right)\] |
| C. | \[\frac{{{I}_{m}}}{5}\left( 1+4co{{s}^{2}}\frac{\phi }{2} \right)\] |
| D. | \[\frac{{{I}_{m}}}{9}\left( 1+8co{{s}^{2}}\frac{\phi }{2} \right)\] |
| Answer» E. | |
| 5020. |
A monochromatic beam of light falls on YDSE apparatus at some angle (say\[\theta \]) as shown figure. A thin sheet of glass is inserted in front of the lower slit\[{{s}_{2}}\]. The central bright fringe (path difference = 0) will be obtained |
| A. | At O |
| B. | Above O |
| C. | Below O |
| D. | Anywhere depending on angle\[\theta \], thickness of plate t, and refractive index of glass\[\mu \] |
| Answer» E. | |
| 5021. |
Blue light of wavelength 480 nm is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incidence. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6, what is the minimum thickness of the oil film (other than zero)? |
| A. | 100 nm |
| B. | 200 nm |
| C. | 300 nm |
| D. | None of these |
| Answer» C. 300 nm | |
| 5022. |
Two Nicols are oriented with their principal planes making an angle of\[60{}^\circ \]. The percentage of incident unpolarized light which passes through the system is |
| A. | 50 % |
| B. | 1 |
| C. | 0.125 |
| D. | 0.375 |
| Answer» D. 0.375 | |
| 5023. |
A plane wave front \[(\lambda =6\times {{10}^{-7}}m)\] falls on a slit 0.4 mm wide. A convex lens of focal length 0.8 m placed behind the slit focusses the light on a screen. What is the linear diameter of second maximum? |
| A. | 6 mm |
| B. | 12 mm |
| C. | 3 mm |
| D. | 9 mm |
| Answer» B. 12 mm | |
| 5024. |
In the ideal double-slit experiment, when a glass plate (refractive index 1.5) of thickness \[t\] is introduced in the path of one of the interfering beams (wavelength\[\lambda \]), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is |
| A. | \[2\lambda \] |
| B. | \[2\lambda /3\] |
| C. | \[\lambda /3\] |
| D. | \[\lambda \] |
| Answer» B. \[2\lambda /3\] | |
| 5025. |
The respective number of significant figures for the numbers 23.023, 0.0003, and 2.1 x \[10_{{}}^{-3}\] are |
| A. | 5, 1, 2 |
| B. | 5, 1, 5 |
| C. | 5, 5, 2 |
| D. | 4, 4, 2 |
| Answer» E. | |
| 5026. |
Number of particles is given by \[n=-D\frac{{{n}_{2}}-{{n}_{1}}}{{{x}^{2}}-{{x}_{1}}}\] crossing a unit area perpendicular to X-axis in unit time, where\[n_{1}^{{}}\]and \[n_{2}^{{}}\] are number of particles per unit volume for the value of \[x_{{}}^{{}}\]meant to \[x_{2}^{{}}\] and \[x_{1}^{{}}\]. Find dimensions of D called as diffusion constant |
| A. | \[M_{0}^{{}}LT_{{}}^{2}\] |
| B. | \[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-4}\] |
| C. | \[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-3}\] |
| D. | \[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-1}\] |
| Answer» E. | |
| 5027. |
In a direct impact, loss in kinetic energy is given by \[\Delta K=\frac{M_{1}^{{}}M_{2}^{{}}}{2(M_{1}^{{}}+M_{2}^{{}})}.(V_{1}^{{}}-V_{2}^{{}})_{{}}^{2}(1-k_{{}}^{2})\] with usual notations (except k). The quantity k will have dimensional formula |
| A. | [\[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-2}\]] |
| B. | [\[M_{{}}^{{}}L_{{}}^{{}}T_{{}}^{-1}\]] |
| C. | [\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}\]] |
| D. | [\[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}\]] |
| Answer» D. [\[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}\]] | |
| 5028. |
While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation \[g=4\pi _{{}}^{2}(l/T_{{}}^{2})\] will be |
| A. | 2% |
| B. | 4% |
| C. | 7% |
| D. | 0.1 |
| Answer» D. 0.1 | |
| 5029. |
If \[m,\text{ }e,\,\,{{\varepsilon }_{0}},\] h and c denote mass electron, charge of electron. Planck's constant and speed of light, respectively. The dimensions of \[\frac{me_{{}}^{4}}{\varepsilon _{0}^{2}h_{{}}^{3}c}\] are |
| A. | [\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{-1}\]] |
| B. | [\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{-1}\]] |
| C. | [\[M_{{}}^{2}L_{{}}^{{}}T_{{}}^{-3}\]] |
| D. | [\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{0}\]] |
| Answer» E. | |
| 5030. |
The wavelength associated with a moving particle depends upon \[{{p}^{th}}\]power of its mass m, \[{{q}^{th}}\]power of its velocity v and \[{{r}^{th}}\] power of Planck's constant h. Then the sum of values of \[p\], q and r is -K. Find the value of K7. |
| A. | 2 |
| B. | 4 |
| C. | 5 |
| D. | 1 |
| Answer» E. | |
| 5031. |
If the acceleration due to gravity is \[10m{{s}^{-2}}\] and the units of length and time are changed in kilometer and hour respectively, what is the numerical value of the acceleration? |
| A. | 129800 |
| B. | 130000 |
| C. | 129600 |
| D. | 128000 |
| Answer» D. 128000 | |
| 5032. |
To determine the Young's modulus of a wire, the formula is \[Y=\frac{F}{A}\times \frac{L}{\Delta L}\]; where L = length, A = area of cross- section of the wire, \[\Delta L\]= change in length of the wire when stretched with a force \[F\]. What is the conversion factor to change it from CGS to MKS system? |
| A. | 0.1 |
| B. | 0.2 |
| C. | 0.3 |
| D. | 0.4 |
| Answer» B. 0.2 | |
| 5033. |
A bus travels distance \[x_{1}^{{}}\]when accelerates from rest at constant rate\[a_{2}^{{}}\]for some time and after that travels a distance\[x_{2}^{{}}\]when decelerates at a constant rate \[a_{2}^{{}}\]to come to rest. A student established a relation \[x_{1}^{{}}+x_{2}^{{}}=\frac{a_{1}^{{}}a_{2}^{{}}t_{{}}^{2}}{2(a_{1}^{{}}+a_{2}^{{}})}\] Choose the correct option(s). |
| A. | The relation is dimensionally correct |
| B. | The relation is dimensionally incorrect |
| C. | The relation may be dimensionally correct |
| D. | None of the above |
| Answer» B. The relation is dimensionally incorrect | |
| 5034. |
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides the main scale line? |
| A. | 0.75 mm |
| B. | 0.80 mm |
| C. | 0.70mm |
| D. | 0.50mm |
| Answer» C. 0.70mm | |
| 5035. |
The dimension of \[{{e}^{2}}/4\pi {{\varepsilon }_{2}}hc,\] where \[e,{{\varepsilon }_{0}},h\] and c are electronic charge, electric permittivity, Planck's constant and velocity of light in vacuum, respectively, is |
| A. | \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] |
| B. | \[[{{M}^{1}}{{L}^{0}}{{T}^{0}}]\] |
| C. | \[[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\] |
| D. | \[[{{M}^{0}}{{L}^{0}}{{T}^{1}}]\] |
| Answer» B. \[[{{M}^{1}}{{L}^{0}}{{T}^{0}}]\] | |
| 5036. |
A body travels uniformly a distance of\[(S+\Delta S)\] in a time \[(t\pm \Delta t)\]. What may be the condition so that body within the error limits move with a velocity \[(\frac{S}{t}\pm \frac{\Delta S}{\Delta t})\]? |
| A. | \[\frac{\Delta t}{t}+\frac{S(\Delta t)_{{}}^{2}}{(\Delta S)t_{{}}^{2}}=\pm 1\] |
| B. | \[\frac{\Delta t}{t}+\frac{S\Delta t_{{}}^{{}}}{\Delta St_{{}}^{{}}}=\pm 1\] |
| C. | \[\frac{\Delta t}{t}+\frac{(\Delta S)t_{{}}^{{}}}{S(\Delta t)_{{}}^{{}}}=\pm 1\] |
| D. | \[\frac{\Delta t}{t}+\frac{S_{{}}^{2}\Delta t_{{}}^{{}}}{(\Delta S)_{{}}^{2}t_{{}}^{{}}}=\pm 1\] |
| Answer» B. \[\frac{\Delta t}{t}+\frac{S\Delta t_{{}}^{{}}}{\Delta St_{{}}^{{}}}=\pm 1\] | |
| 5037. |
The position of a particle at time \[t\]is given by the relation \[x(t)=(\frac{v_{0}^{{}}}{\alpha })(1-c_{{}}^{-\alpha t})\]where \[v_{0}^{{}}\] ls a constant and a > 0. The dimensions of \[v_{0}^{{}}\] and \[\alpha \] are respectively |
| A. | \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,T_{{}}^{-1}\] |
| B. | \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{0}and\,T_{{}}^{-1}\] |
| C. | \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,LT_{{}}^{-2}\] |
| D. | \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,LT_{{}}^{{}}\] |
| Answer» B. \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{0}and\,T_{{}}^{-1}\] | |
| 5038. |
Which of the following product of \[e,h,\mu ,G\](where \[\mu \]is the permeability) be taken so that the dimensions of the product are same as that of the speed of light? |
| A. | \[he_{{}}^{-2}\mu _{{}}^{-1}G_{{}}^{0}\] |
| B. | \[h_{{}}^{2}eG_{{}}^{0}\mu \] |
| C. | \[h_{{}}^{0}e_{{}}^{2}G_{{}}^{-1}\mu \] |
| D. | \[hGe_{{}}^{-2}\mu _{{}}^{0}\] |
| Answer» B. \[h_{{}}^{2}eG_{{}}^{0}\mu \] | |
| 5039. |
If force F, acceleration a, and time T are taken as the fundamental physical quantities, the dimensions of length on this system of units, are |
| A. | \[FAT_{{}}^{2}\] |
| B. | FAT |
| C. | FT |
| D. | \[AT_{{}}^{2}\] |
| Answer» E. | |
| 5040. |
The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is \[W_{1}^{{}}\] = \[8.00\text{ }\pm \text{ }0.05\text{ }N\]and the weight in water is \[W_{2}^{{}}\] = \[6.00\text{ }\pm \text{ }0.05\] N, then the relative density \[\rho _{r}^{{}}=W_{1}^{{}}/(W_{1}^{{}}-W_{2}^{{}})\] With the maximum permissible error is |
| A. | \[4.00\text{ }\pm 0.62\]% |
| B. | \[4.00\text{ }\pm 0.82\]% |
| C. | \[4.00\text{ }\pm 3.2\]% |
| D. | \[4.00\text{ }\pm 5.62\]% |
| Answer» E. | |
| 5041. |
The potential energy of a particle varies with distance \[\chi \] as \[U=\frac{Ax_{{}}^{1/2}}{x_{{}}^{2}+B}\] where A and B are constants. The dimensional formula for A x B is |
| A. | \[M_{{}}^{1}L_{{}}^{7/2}T_{{}}^{-2}\] |
| B. | \[M_{{}}^{1}L_{{}}^{1/2}T_{{}}^{-2}\] |
| C. | \[M_{{}}^{1}L_{{}}^{5/2}T_{{}}^{-2}\] |
| D. | \[M_{{}}^{1}L_{{}}^{9/2}T_{{}}^{-2}\] |
| Answer» C. \[M_{{}}^{1}L_{{}}^{5/2}T_{{}}^{-2}\] | |
| 5042. |
If \[F=\frac{v}{C\ln (xb)}\], then |
| A. | F and v denote force and velocity, the dimensions of C are [MT] |
| B. | x denotes distance, the dimensions of b are [\[L_{{}}^{-1}\]] |
| C. | The dimension of \[\frac{v}{C}\] never be same as F |
| D. | The dimensions of x must be same as \[\frac{v}{cb}\] |
| Answer» C. The dimension of \[\frac{v}{C}\] never be same as F | |
| 5043. |
A particle is executing a motion in which its displacement as a function of time is given by \[x=3\,\sin \,(5\pi t+\pi /3)+cos(5\pi t+\pi /3)\]where \[x\] is in \[m\] and \[t\] is in s. Then the motion is |
| A. | Simple harmonic with time period 0.2 s |
| B. | Simple harmonic with time period 0.4 s |
| C. | Simple harmonic with amplitude 3 m |
| D. | Not a simple harmonic but a periodic motion |
| Answer» C. Simple harmonic with amplitude 3 m | |
| 5044. |
Two identical springs are attached to a small block\[p\]. The other ends of the springs are fixed at \[A\] and\[B\]. When \[p\]the extension of top spring is in equilibrium is 20 cm and extension p of bottom spring is 10 cm. The period of small vertical oscillations of? about its equilibrium position is (use \[g=9.8\,m/{{s}^{2}}\]) |
| A. | \[\frac{2\pi }{7}\sec \] |
| B. | \[\frac{\pi }{7}\sec \] |
| C. | \[\frac{2\pi }{5}\sec \] |
| D. | none of these |
| Answer» C. \[\frac{2\pi }{5}\sec \] | |
| 5045. |
A body is executing Simple Harmonic Motion. At a displacement \[x\] its potential energy is \[{{E}_{1}}\] and at a displacement \[y\] its potential energy is \[{{E}_{2}}\] The potential energy \[E\] at displacement \[(x+y)\]is |
| A. | \[\sqrt{E}=\sqrt{{{E}_{1}}}-\sqrt{{{E}_{2}}}\] |
| B. | \[\sqrt{E}=\sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}\] |
| C. | \[E={{E}_{1}}+{{E}_{2}}\] |
| D. | \[E={{E}_{1}}-{{E}_{2}}\] |
| Answer» C. \[E={{E}_{1}}+{{E}_{2}}\] | |
| 5046. |
A particle perfroms SHM with a period \[T\] and amplitude \[a\]The mean velocity of the particle over the time interval during which it travels a distance all from the extreme position is |
| A. | \[a/T\] |
| B. | \[2a/T\] |
| C. | \[3a/T\] |
| D. | \[a/2T\] |
| Answer» D. \[a/2T\] | |
| 5047. |
Two particles move parallel to the \[x\]-axis about the origin with same amplitude '\[a\]' and frequency\[\omega \]. At a certain instant they are found at a distance \[a/3\] from the origin on opposite sides but their velocities are in the same direction. What is the phase difference between the two? |
| A. | \[{{\cos }^{-1}}\frac{7}{9}\] |
| B. | \[{{\cos }^{-1}}\frac{5}{9}\] |
| C. | \[{{\cos }^{-1}}\frac{4}{9}\] |
| D. | \[{{\cos }^{-1}}\frac{1}{9}\] |
| Answer» B. \[{{\cos }^{-1}}\frac{5}{9}\] | |
| 5048. |
A vertical mass-spring system executes simple harmonic oscillations with a period of \[2s.\,A\] quantity of this system which exhibits simple harmonic variation with a period of 1 s is |
| A. | Velocity |
| B. | Potential energy |
| C. | Phase difference between acceleration and dis- placement |
| D. | Difference between kinetic energy and potential energy |
| Answer» C. Phase difference between acceleration and dis- placement | |
| 5049. |
Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by\[45{}^\circ \], then |
| A. | The resultant amplitude is\[\sqrt{2}a\] |
| B. | The phase of the resultant motion relative to the first is \[90{}^\circ \] |
| C. | The energy associated with the resulting motion is \[(3+2\sqrt{2})\] times the energy associated with any single motion |
| D. | The resulting motion is not simple harmonic |
| Answer» D. The resulting motion is not simple harmonic | |
| 5050. |
An object of mass \[0.2kg\] executes simple harmonic along \[X\]-axis with frequency of \[\frac{25}{\pi }Hz\]. At the position x = 0.04 m, the object has kinetic energy of 0.5 J and potential energy of 0.4 J. The amplitude of oscillation in meter is equal to |
| A. | 0.05 |
| B. | 0.06 |
| C. | 0.01 |
| D. | None of these |
| Answer» C. 0.01 | |