Q. A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is $4J$ then total kinetic energy of the disc is

1. $3J$
2. $4J$
3. $5J$
4. $6J$

Q. In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is

1. 5
2. 2
3. 0.5
4. 0.2

Q. Let 'M' be the mass and 'L' be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is

1. $\frac{1}{2}$
2. $1$
3. $\frac{1}{8}$
4. $\frac{1}{4}$

Q. Two stings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed '$V_A$' and on string B with speed '$V_B$'. The ratio $\frac{V_A}{V_B}$ is

1. $\frac{1}{4}$
2. $\frac{1}{2}$
3. $2$
4. $4$

Q. In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire x cm long. If the length of the potentiometer wire is increased without changing the cell, the balancing length will (Driving source is not changed)

1. increase
2. decrease
3. becomes zero
4. not change

Q. An electron of mass 'm' has de-Broglie wavelength '$\lambda$' when accelerated through potential difference 'V'. When proton of mass 'M', is accelerated through potential difference $9V$, the de-Broglie wavelength associated with it will be : (Assume that wavelength is determined at low voltage)

1. $\frac{\lambda }{3}\sqrt{\frac{M}{m}}$
2. $\frac{\lambda }{3}.\frac{M}{m}$
3. $\frac{\lambda }{3}\sqrt{\frac{m}{M}}$
4. $\frac{\lambda }{3}.\frac{m}{M}$

Q. A black rectangular surface of area 'A' emits energy 'E' per second at 27${}^o$C. If length and breadth are reduced to $\frac{1}{3}rd$ of initial value and temperature is raised to 327${}^o$C then energy emitted per second becomes

1. $\frac{16E}{9}$
2. $\frac{7E}{9}$
3. $\frac{10E}{9}$
4. $\frac{4E}{9}$

Q. For a gas $\frac{R}{C_v}=0.4$, where 'R' is the universal gas constant and 'C${}_v$' is molar specific heat at constant volume. The gas is made up of molecules which are

1. rigid diatomic
2. monoatomic
3. non-rigid diatomic
4. polyatomic

Q. When the observer moves towards the stationary source with velocity, 'V${}_1$', the apparent frequency of emitted note is 'F${}_1$'. When the observer moves away from the source with velocity 'V${}_1$', the apparent frequency is 'F${}_2$'. If 'V' is the velocity of sound in air and $\frac{F_1}{F_2}=2$ then, $\frac{V}{V_1}$?

1. 3
2. 2
3. 5
4. 4

Q. An iron rod is placed parallel to the magnetic field of intensity 2000 A/m. The magnetic flux through the rod is $6\times {10}^{-4}Wb$ and its cross-sectional area is 3 cm${}^2$. The magnetic permeability of the rod in $\frac{Wb}{A-m}$ is:

1. ${10}^{-1}$
2. ${10}^{-2}$
3. ${10}^{-3}$
4. ${10}^{-4}$

Q. Which of the following quantity does not change due to damping of oscillations?

1. Angular frequency
2. Time period
3. Initial phase
4. Amplitude

Q. Let a steel bar of length '$l$', breadth 'b' and depth 'd' be loaded at the centre by a load 'W'. Then the sag of bending of beam is (Y = Young's modulus of material of steel)

1. $\frac{W{l}^3}{2b{d}^{3}Y}$
2. $\frac{W{l}^3}{4b{d}^{3}Y}$
3. $\frac{W{l}^2}{2b{d}^{3}Y}$
4. $\frac{W{l}^3}{4b{d}^{2}Y}$

Q. A particle moves along a circle of radius '$r$' with constant tangential acceleration. If the velocity of the particle is '$v$' at the end of second revolution, after the revolution has started then the tangential acceleration is

1. $\frac{v^2}{4\pi r}$
2. $\frac{v^2}{6\pi r}$
3. $\frac{v^2}{8\pi r}$
4. $\frac{v^2}{2\pi r}$

Q. Two particles of masses 'm' and '9m' are separated by a distance 'r'. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is (G = Universal constant of gravitation)

1. $-\frac{4Gm}{r}$
2. $-\frac{8Gm}{r}$
3. $-\frac{16Gm}{r}$
4. $-\frac{32Gm}{r}$

Q. A simple pendulum of length '$l$' has maximum angular displacement '$\theta$'. The maximum kinetic energy of the bob of mass 'm' is :
(g = acceleration due to gravity)

1. $mgl(1+cos\theta )$
2. $mgl(1+co{s}^2\theta )$
3. $mgl(1-cos\theta )$
4. $mgl(cos\theta -1)$

Q. A progressive wave is represented by y = 12 sin (5t - 4x) cm. On this wave, how far away are the two points having phase difference of 90${}^o$?

1. $\frac{\pi }{2}cm$
2. $\frac{\pi }{4}cm$
3. $\frac{\pi }{8}cm$
4. $\frac{\pi }{16}cm$

Q. Interference fringes are produced on a screen by using two light sources of intensities 'I' and '9I'. The phase difference between the beams is $\frac{\pi }{2}$ at point P and $\pi$ at point Q on the screen. The difference between the resultant intensities at point P and Q is :

1. $2I$
2. $4I$
3. $6I$
4. $8I$

Q. Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1 : 3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is

1. 81 : 1
2. 27 : 1
3. 9 : 1
4. 3 : 1

Q. A disc of radius 'R' and thickness $\frac{R}{6}$ has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

1. $\frac{I}{5}$
2. $\frac{I}{6}$
3. $\frac{I}{32}$
4. $\frac{I}{64}$

Q. Angular speed of the hour hand of a clock in degree per second is :

1. $\frac{1}{30}$
2. $\frac{1}{720}$
3. $\frac{1}{60}$
4. $\frac{1}{120}$

Q. A liquid drop having surface energy '$E$' is spread into $512$ droplets of same size. The final surface energy of the droplets is

1. $2E$
2. $4E$
3. $8E$
4. $12E$

Q. Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be

1. 186 Hz
2. 280 Hz
3. 256 Hz
4. 225 Hz

Q. When an open pipe is closed from one end then third overtone of closed pipe is higher in frequency by 150 Hz than second overtone of open pipe. The fundamental frequency of open end pipe will be

1. 150 Hz
2. 75 Hz
3. 225 Hz
4. 300 Hz

Q. Alternating current of peak value $\left(\frac{2}{\pi }\right)$ ampere flows through the primary coil of the transformer. The coefficient of mutual inductance between primary and secondary coil is 1 henry. The peak e.m.f. induced in secondary coil is
(Frequency of a.c. = 50 Hz)

1. 100 V
2. 200 V
3. 300 V
4. 400 V

Q. A mass '$m_1$' connected to a horizontal spring performs S.H.M. with amplitude 'A'. While mass '$m_1$' is passing through mean position another mass '$m_2$' is placed on it so that both the masses move together with amplitude '$A_1$'. The ratio of $\frac{A_1}{A}$ is $(m_2<m_1)$

1. ${\left[\frac{m_2}{m_1+m_2}\right]}^{\frac{1}{2}}$
2. ${\left[\frac{m_1+m_2}{m_1}\right]}^{\frac{1}{2}}$
3. ${\left[\frac{m_1}{m_1+m_2}\right]}^{\frac{1}{2}}$
4. ${\left[\frac{m_1+m_2}{m_2}\right]}^{\frac{1}{2}}$

Q. If the end correction of an open pipe is 0.8 cm then the inner radius of that pipe will be

1. $\frac{1}{3}$ cm
2. $\frac{2}{3}$ cm
3. $\frac{3}{2}$ cm
4. $0.2$ cm

Q. Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is

1. ${\left[\frac{2}{3}\right]}^{rd}$ kinetic energy per unit volume of a gas
2. ${\left[\frac{1}{3}\right]}^{rd}$ kinetic energy per unit volume of a gas
3. $\frac{3}{2}\times$ kinetic energy per unit volume of a gas
4. ${\left[\frac{3}{3}\right]}^{th}$ kinetic energy per unit volume of a gas

Q. The bob of a simple pendulum performs S.H.M. with period 'T' in air and with period '$T_1$' in water. Relation between 'T' and '$T_1$' is (neglect friction due to water, density of the material of the bob is $\frac{9}{8}\times {10}^{3}kg/m^3,$ density of water = 1 g/cc)

1. $T_1=3T$
2. $T_1=2T$
3. $T_1=\frac{T}{2}$
4. $T_1=T$

Q. In a capillary tube of radius 'R', a straight thin metal wire of radius 'r' (R > r) is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is [T = surface tension of water, $\rho$ = density of water, g = gravitational acceleration]

1. $\frac{T}{(R+r)\rho g}$
2. $\frac{R\rho g}{2T}$
3. $\frac{2T}{(R-r)\rho g}$
4. $\frac{(R-r)\rho g}{T}$

Q. The value of gravitational acceleration 'g' at a height 'h' above the earth's surface is $\frac{g}{4}$ then (R = radius of earth)

1. $h=\frac{R}{2}$
2. $h=R$
3. $h=\frac{R}{3}$
4. $h=\frac{R}{4}$