The block of mass $M$ moving on the frictionless horizontal surface collides with a spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is
(1) $\sqrt{\mathrm{MK}}\,\mathrm{L}$
(2) $\frac{\mathrm{KL}^2}{2\mathrm{M}}$
(3) zero
(4) $\frac{ML^2}{\mathrm{K}}$

A block of mass 0.50 kg is moving with a speed of $2.00 \mathrm{~m/s}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
(1) 0.16 J
(2) 1.00 J
(3) 0.67 J
(4) 0.34 J

A moving particle of mass $m$, makes a head on elastic collision with another particle of mass $2m$, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to
(1) $33 \%$
(2) $67 \%$
(3) $90 \%$
(4) $10 \%$

A spring is compressed between two blocks of masses $m_{1}$ and $m_{2}$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_{1}$ and $v_{2}$ as shown. The blocks travel distances $x_{1}$ and $x_{2}$ respectively before coming to rest. The ratio $\left(\frac{x_{1}}{x_{2}}\right)$ is
(1) $\frac{m_{2}}{m_{1}}$
(2) $\frac{m_{1}}{m_{2}}$
(3) $\sqrt{\frac{m_{2}}{m_{1}}}$
(4) $\sqrt{\frac{m_{1}}{m_{2}}}$

Three masses $\mathrm{m}$, $2\mathrm{m}$ and $3\mathrm{m}$ are moving in $\mathrm{x}$-$\mathrm{y}$ plane with speed $3\mathrm{u}$, $2\mathrm{u}$ and $\mathrm{u}$ respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be:
(1) $\frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})$
(2) $\frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})$
(3) $\frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})$
(4) $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$

A simple pendulum, made of a string of length $l$ and a bob of mass $m$, is released from a small angle $\theta _ { 0 }$. It strikes a block of mass $M$, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $\theta _ { 1 }$. Then $M$ is given by:
(1) $m \left( \frac { \theta _ { 0 } - \theta _ { 1 } } { \theta _ { 0 } + \theta _ { 1 } } \right)$
(2) $m \left( \frac { \theta _ { 0 } + \theta _ { 1 } } { \theta _ { 0 } - \theta _ { 1 } } \right)$
(3) $\frac { m } { 2 } \left( \frac { \theta _ { 0 } + \theta _ { 1 } } { \theta _ { 0 } - \theta _ { 1 } } \right)$
(4) $\frac { m } { 2 } \left( \frac { \theta _ { 0 } - \theta _ { 1 } } { \theta _ { 0 } + \theta _ { 1 } } \right)$

Two particles of masses $M$ and 2 M are moving with speeds of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds $v _ { 1 }$ and $v _ { 2 }$, respectively. The values of $v _ { 1 }$ and $v _ { 2 }$ are, nearly
(1) $6.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $12.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $13.02 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $19.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $6.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

A man (mass $= 50$ kg) and his son (mass $= 20$ kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70 \text{ m s}^{-1}$ with respect to the man. The speed of the man with respect to the surface is:
(1) $0.20 \text{ m s}^{-1}$
(2) $0.14 \text{ m s}^{-1}$
(3) $0.47 \text{ m s}^{-1}$
(4) $0.28 \text{ m s}^{-1}$

Three blocks $\mathrm { A } , \mathrm { B }$ and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, $m$ while C has mass $M$. Block A is given an initial speed $v$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically . $\frac { 5 } { 6 }$ th of the initial kinetic energy is lost in the whole process. What is the value of $M / m$ ?
(1) 3
(2) 4
(3) 5
(4) 2

A body A of mass $m = 0.1 \mathrm {~kg}$ has an initial velocity of $3 \hat { \mathrm { i } } \mathrm { m s } ^ { - 1 }$. It collides elastically with another body B of the same mass which has an initial velocity of $5 \hat { \mathrm { j } } \mathrm { m s } ^ { - 1 }$. After the collision, A moves with a velocity $\vec { v } = 4 ( \hat { \mathrm { i } } + \hat { \mathrm { j } } ) \mathrm { m s } ^ { - 1 }$. The energy of B after the collision is written as $\frac { x } { 10 } \mathrm {~J}$. The value of $x$ is $\_\_\_\_$.

Three objects $A , B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A , B$ and $C$ are $m , 2 m$ and $2 m$ respectively. $A$ moves towards $B$ with a speed of $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is:
(1) $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be
(1) $1 : 1$
(2) $2 : 1$
(3) $1 : 4$
(4) $4 : 1$

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1 : 1 : 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. The velocity of the third piece will be
(1) $35 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then the trolly car starts moving with velocity $2\mathrm{~m\,s^{-1}}$. The velocity of the running man was $\_\_\_\_$ $\mathrm{m\,s^{-1}}$, when he jumps into the car.

Two bodies are having kinetic energies in the ratio $16:9$. If they have same linear momentum, the ratio of their masses respectively is:
(1) $3:4$
(2) $9:16$
(3) $16:9$
(4) $4:3$