Exercises

Two blocks of masses $\mathrm{m}$ and $4 \mathrm{m}$ lie on a smooth horizontal surface connected with a spring in its natural length. Mass $\mathrm{m}$ is given velocity $v_0$ through an impulse as shown in figure. Which of the following is not true about subsequent motion?

Two identical blocks, having mass $\mathrm{M}$ each, are conjugated and placed on a smooth floor as shown in figure. A small block of mass $\mathrm{m}$ is released from position as shown. Velocity of block $\mathrm{B}$ is maximum

In figure, a hollow tube of mass $\mathrm{M}$ is free in horizontal direction. The system is released from rest. There is no friction present. The tube and blocks are taken as system.

i. Momentum of the system is conserved in $\mathrm{x}$ -direction.
ii. Speed of $\mathrm{A}$ w.r.t. $\mathrm{M}=$ Speed of $\mathrm{B}$ w.r.t. $\mathrm{M}$

¡ii. Trajectory of centre of mass is $\mathrm{X}$ -constant. iv. Centre of mass has finite acceleration.
Evaluate the above statements and choose the correct option from the following:

A trolley is moving horizontally with a velocity of $v \mathrm{m}/\mathrm{s}$ w.r.t. earth. A man starts running in the direction of motion of trolley from one end of the trolley with a velocity $1.5\mathrm{v}$ $\mathrm{m}/\mathrm{s}$ w.r.t. the trolley. After reaching the opposite end, the man turns back and continues running with a velocity of $1.5$ $v \mathrm{m}/\mathrm{s}$ w.r.t. trolley in the backward direction. If the length of the trolley is $L,$ then the displacement of the man with respect to earth, measured as a function of time, will attain a maximum value of 

Two blocks of masses ${\mathrm{m}}_1=2 \mathrm{kg}$ and ${\mathrm{m}}_2=4 \mathrm{kg}$ are moving in the same direction with speeds ${\mathrm{v}}_1=6 \mathrm{m}/\mathrm{s}$ and ${\mathrm{v}}_2=3 \mathrm{m}/\mathrm{s},$ respectively on a frictionless surface as shown in the figure. An ideal spring with spring constant $\mathrm{k}=30000$ $\mathrm{N}/\mathrm{m}$ is attached to the back side of ${\mathrm{m}}_2.$ Then the maximum compression of the spring after collision will be

Block $\mathrm{A}$ is released on the circular track of bigger block $\mathrm{B}$ from rest from the position as shown in figure. Friction is absent everywhere. Choose the correct statement.

Two identical particles $A$ and $B$ of mass $\mathrm{m}$ each are connected together by a light and inextensible string of length $l.$ The particle are held at rest in air in same horizontal level at a separation $l.$ Both particles are released simultaneously and one of them (say$A$ ) is given speed $v_0$ vertically upward. The maximum height attained by the centre of mass of the system of $A$ and $B$ from initial level is (Ignore air resistance). 

A particle of mass $\mathrm{m}=0.2 \mathrm{kg}$ is released from rest from a point $\mathrm{A}$ of a triangular wedge of mass $\mathrm{M}=4.8 \mathrm{kg}$ free to slide on a frictionless horizontal plane. The particle slides down the smooth face $\mathrm{AB}$ of the wedge. When the velocity of the wedge is $0.1 \mathrm{m} {\mathrm{s}}^{-1},$ the velocity of the particle in $\mathrm{m} {\mathrm{s}}^{-1}$ relative to the wedge is