B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 58: CONCEPT APPLICATION EXERCISE 8.4

In the figure, an inextensible string that connects two bodies of mass $M$ and $m$, passing over a fixed smooth pulley. The body $M$ slides along a smooth vertical rigid bar. If the body $M$ is released from the given position, find the maximum distance raised by body $m$.

Two smooth balls of mass $m_1$ and $m_2$ connected by a light inextensible string are at the opposite points of horizontal diameter of a smooth semi cylindrical surface of radius $R$. If $m_1$ is released, find its speed at any angular distance $\theta$ moved by $m_2$.

A spring-mass system $\left(m_1+\mathrm{massless} \mathrm{spring}+m_2\right)$ fall freely from a height $h$ before $m_2$ colliding inelastically with the ground. Find the maximum value of $h$ so that block $m_2$ will break off the surface. Assume $k=$ stiffness of the spring.

In an ideal pulley particle system, the mass $m_2$ is connected with a vertical spring of stiffness $k$. If the mass $m_2$ is released from rest, when the spring is deformed, find the maximum compression of the spring.

The figure below shows two blocks of masses $2M$ and $M$, respectively. The coefficient of friction between the block of mass $2M$ and the horizontal plane is $\mu$. The system is released from rest. Find the velocity of the block of mass $M$, when the block of mass $2M$ has moved a distance $s$ towards the right.

In the figure shown, the system is released from the rest. Find the velocity of the block $A$ when the block $B$ has fallen a distance $l$. Assume all pulleys to be massless and frictionless.

In the figure shown, a skateboarder is moving at $5.0 \mathrm{m} {\mathrm{s}}^{-1}$ along the horizontal section of a track that is slanted upward by $60°$ above the horizontal at its end, which is $0.45 \mathrm{m}$ above the ground. When he leaves the track, he follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height $H$ to which he rises above the end of the track.

In the fig shown, a block of mass $M$ is attached to the spring and another block of mass $2M$ has been placed over it. The system is in equilibrium. The block are pushed down so that the spring compresses further by $\frac{9Mg}{K}$. System is released.

(a) At what height above the position of release, the block of mass $2M$ will lose contact with the other block?

(b) What is maximum height attained by $2M$ above the point of release?