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Q 1.

A cylinder moves with linear velocity v to the right and angular velocity \(\omega\) in the anticlockwise direction at a particular instant of time t. The cylinder was initially at rest. The cylinder does not perform pure rolling and stops after some time. Find radius of the cylinder

Q 2.
If resistance \(R = (100 ± 5)\Omega\) and current I = (10 ± 0.2) A. The percentage error in thermal power (\(P = I^2R\)) is

Q 3.
A disc of mass \(m\) and radius\( r\) is rolling with an angular velocity \(\omega\) on a horizontal plane. The magnitude of angular momentum of the disc about the origin \(O\) is\(\frac3 4 \)\(\frac{v}{\omega}\)

Q 4.
If a particle moving in a straight line with uniform acceleration starting from rest covers displacement \(S_1\) in \(p^{th}\) second and displacement \(s_2\) in \((p + 1)^{th}\) second, then the displacemen t upto p seconds is given by

Q 5.

A block is hanging at one end of the massless rope passing over a fixed smooth pulley. From the other end of the rope a man of same mass climbs with an acceleration x relative to the rope. If acceleration of block is a, find the value of x.

Q 6.

Following graph is plotted between displacement and time. Its acceleration is best described as (where b, c are +ve constants)

Q 7.
A bullet penetrates a plank with initial velocity \( v_1\) and comes out with velocity \( v_2\). Another similar bullet penetrates the same plank with initial velocity \(v_2 \)and still comes out with some velocity provided

Q 8.
A particle is moving in uniform circular motion with speed v of radius R. The ratio of average velocity to average acceleration in half of the circle

Q 9.
A man is standing on a stationary car of mass \(m\) placed on a smooth rail. The man starts walking with velocity \(v\) relative to car. Find the mass of the man if work done by him when he moves along the rails is same when he walks normal to the rails

Q 10.
A particle is moving in a circular motion of radius\( R\). Its tangential retardation at any time is equal to the centripetal acceleration. If it starts with speed\( v0\), then the speed after one revolution is

Q 11.

A simple pendulum of length \(L\), time period \(T\) is suspended from\( O\) such a way that an obstacle touches its string vertically below at distance y in its equilibrium position. If pendulum is defelected slightly to the right and released, it come back to intial position after time \(\frac{5T}8\) , value of y is

Q 12.
A particle starts moving with velocity \(\vec{V}(Y^2\check{i}+x\check{j})\) from origin, where k is a constant. The general equation for its path is

Q 13.

In the syphon are shown which of the option is not correct if \(h_2 > h_1\) and \(h_3 < h_1? \)

Q 14.
A stationary body of mass 3 kg explodes in to three pieces of equal mass. Two of the piece fly off along x-axis and yaxis with equal speed 2 m/s and time of explosion is \(10^{–3}\) s, then average force on the third piece

Q 15.
A cylindrical tube open at both ends has fundamental frequency\( f \)in air. Half of the length of the tube is dipped vertically in water. The fundamental frequency of the air column now is

Q 16.
Two particles of equal mass are moving along x-axis and y-axis respectively, if initial velocity of 1st particle is zero but acceleration is constant whereas 2nd particle acceleration is zero, then path of centre of mass

Q 17.

Find the workdone by the gas in the process ABC.

Q 18.
A rocket is sent vertically up with a velocity \(v =\sqrt{gR}\) from earth surface, where symbols have usual meaning. The maximum height reached will be

Q 19.

A convex and a concave lens are coaxially placed. The object is placed to the left of convex lens of focal length 20 cm. The final image is formed at infinity. The focal length of concave lens is 5 cm. The distance between two lenses may be

Q 20.
If Young’s modulus of a wire is \(Y = 10^{10} N/m^2\), and strain on it is 0.001, then the energy stored in wire per unit volume is

Q 21.
A projectile is projected at a velocity 50 m/s at an angle of 30° with horizontal. Find the magnitude of change in velocity in 2 seconds. (\(g = 10 m/s ^2\))
Q 22.
In an ideal gas at constant pressure change in internal energy is double of the work done by gas, the degree of freedom of gas is
Q 23.
If the atom \(_{100}Fm^{257}\) follows the Bohr’s model and the radius of \(_{100}Fm^{257}\) is n times the Bohr’s radius then find n.
Q 24.
A glass containing a liquid appears to be half filled when viewed from top, if it is actually two-thirds filled. The refractive index of liquid is
Q 25.
Energy required to remove both the electrons of helium is 79 eV. Find the binding energy of an electron in the ground state of He.
Q 26.
If 25% part of length of wire is stretched by 25%, then percentage change in resistance of wire will be about
Q 27.
The equation of motion of a particle is given by x = 5 + 3 sin (\(\pi{t}\)), where x is in cm and t is in seconds. Find the position of particle at time equal to one fourth of the time period of motion (in cm)
Q 28.
A boat in a pond undergoes a wave bounces 20 times in a minute. If velocity of transverse wave is 25 m/s, then distance between succesive crest and trough will be
Q 29.
In a resonance tube the first and second resonance are obtained at 20.1 cm and 60.5 cm. The third resonance will be obtained at
Q 30.

 A particle of mass m is moving along the x-axis with initial velocity \(u\hat i\) . It collides elastically with a particle of mass \(10m\) at rest and then moves with half its initial kinetic energy (see figure). If \(sin\theta_1=\sqrt{n}\sin\theta_2\) then value of n is ________.

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