Two masses ' $A$ ' and ' $B$ ' having mass $\mathrm{m}$ and $2\mathrm{m}$ respectively are kept on a smooth horizontal table as shown in the figure. The mass ' $B$ ' is given a velocity $v$ perpendicular to the string parallel to the table. If $m=0.3 \mathrm{kg}, v=5 \mathrm{m}/\mathrm{s}$ and $l=1 \mathrm{m},$ then find the tension in the string (in $N$ ).

In the figure shown a small block $B$ of mass $\mathrm{m}$ is released from the top of a smooth movable wedge $A$ of the same mass $\mathrm{m}.$ The height of wedge -shown in figure is $h=100 \mathrm{cm}.B$ ascends another movable smooth wedge $C$ of the same $\mathrm{m}.$ Neglecting friction any where, find the maximum height (in $\mathrm{cm}$ ) attained by block $B$ on wedge $C.$

In the figure shown initially spring is in relaxed state and blocks are at rest. Now $100 \mathrm{N}$ force is applied on block $A$ and $B$ as shown in figure. After some time velocity of ' $A$ ' becomes $2 \mathrm{m}/\mathrm{s}$ and that of ' $B$ ' $4 \mathrm{m}/\mathrm{s}$ and block $A$ displaced by amount $10 \mathrm{cm}$ towards left and spring is stretched by amount $30 \mathrm{cm}.$ Then work done by spring force on $A$ is $W_0$ joule. Find $\left|W_0\right|$ (in $\mathrm{J}$).

A ring of mass $M=90 \mathrm{g}$ and radius $R=3 \mathrm{m}$ is kept on a frictionless horizontal surface such that its plane is parallel to horizontal plane. A particle of mass $m=10 \mathrm{g}$ is placed in contact with the inner surface of ring as shown figure. An initial velocity $v=\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ is given to the particle along the tangent of the ring. Find the magnitude of the force of interaction (in milli-newton) between the particle and ring.

Two particles $P$ and $Q$ have mass $4.0 \mathrm{kg}$ and $1 \mathrm{kg}$ respectively. They are projected along a vertical line with velocity $u_P=$ $20 \mathrm{m} {\mathrm{s}}^{-1}$ and $u_Q=5 \mathrm{m} {\mathrm{s}}^{-1}$ when separation between them was $60 \mathrm{m}. P$ was projected vertically up while $Q$ was projected vertically down. Calculate the maximum height attained (in $\mathrm{m}$ ) by the centre of mass of the system of two particles, measured from the initial position of $P.$ Assume that the particles do not collide and that the ground is far below their point of projection $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}\right].$

Two blocks of masses $\mathrm{m}=2 \mathrm{kg}$ and $M=8 \mathrm{kg}$ are connected to a spring of force constant $k=1\mathrm{kN}/\mathrm{m}.$ The spring is compressed by $20 \mathrm{cm}$ and the two blocks are held in this position by a string. The system is placed on a horizontal smooth surface and given a velocity $u=3 \mathrm{m}/\mathrm{s}$ perpendicular to the spring. The string snaps while moving. The speed (in $\mathrm{m}/\mathrm{s}$ ) of the block of mass $\mathrm{m}$ when the spring regains its natural length is

Three identical particles are placed on a horizontal smooth table, connected with strings as shown. The particle $B$ is imparted a velocity $v_0=9 \mathrm{m}/\mathrm{s}$ in horizontal direction perpendicular to the line $ABC.$ The speed (in $\mathrm{m}/\mathrm{s}$ ) of particle $A$ when it is about to collide with $C.$