A mass attached to one end of a string crosses top-most point on a vertical circle with critical  speed, its centripetal acceleration when string becomes horizontal  will be (where, g= gravitational acceleration)

A) g

B) 3g

C) 4g

D) 6g


A bomb at rest explodes into 3 parts of same mass . The momentum of two parts is -3 p $\hat{i}$ and 2p$\hat{j}$ , respectively . The magnitude of momentum of the third part is 

A) p

B) $\sqrt{5}p$

C) $\sqrt{11}p$

D) $\sqrt{13}p$


The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is l. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it, so that their centres coincide. If  both the rings are rotating  about the same axis, then loss in kinetic energy is 

A) $\frac{l\omega^{2}}{2}$

B) $\frac{l\omega^{2}}{4}$

C) $\frac{l\omega^{2}}{6}$

D) $\frac{l\omega^{2}}{8}$


Magnetic susceptibility for a paramagnetic and diamagnetic materials is respectively

A) small, positive and small, positive

B) large, positive and small, negative

C) small, positive and small, negative

D) large, negative and large, positive


Asquare frame ABCD is formed by four identical rods each of mass m and length l, This frame is in

XY- plane such that side AB coincides with X-axis and side AD along Y- axis. The moment of inertia of the frame about X-axis is 

A) $\frac{5ml^{2}}{3}$

B) $\frac{2ml^{2}}{3}$

C) $\frac{4ml^{2}}{3}$

D) $\frac{ml^{2}}{12}$