B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 70: Exercises

Two springs $P$ and $Q$, having stiffness constants $K_1$ and $K_2$ $\left(K_2<K_1\right)$ respectively. If equal forces are applied on two springs, then,

A ball released at $AA$ leaves the frictionless track at $B$, which is at a height of $3 \mathrm{m}$ from the ground. The ball further rises maximum up to $4 \mathrm{m}$ above the ground before falling down. Find $h (\mathrm{in} \mathrm{m})$ if the track at $B$ makes an angle of $30°$ with the horizontal.

Two objects are connected by a light string passing over a light, frictionless pulley as shown in the figure. The object of mass $m_1=5.0 \mathrm{kg}$ is released from rest at a height $h=4.0 \mathrm{m}$ above the table. Find the maximum height above the table to which the $3.0 \mathrm{kg}$ object rises (in $\mathrm{m}$).

In the figure, the variation of components of acceleration of a particle of mass $1 \mathrm{kg}$ is shown w.r.t. time. The initial velocity of the particle is $\overrightarrow{u}=\left(-3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Find the total work done by the resultant force on the particle in the time interval from $t=0$ to $t=4$ seconds in $\mathrm{J}$.

As shown in the figure, there is no friction between the horizontal surface and the lower block $(M=3 \mathrm{kg})$ but the friction coefficient between both the blocks is $0.2$. Both the blocks move together with initial speed $V$ towards the spring, compresses it and due to the force exerted by the spring, moves in the reverse direction of the initial motion. Find the maximum value of $V (\mathrm{in} \mathrm{cm} {\mathrm{s}}^{-1})$ so that during the motion, there is no slipping between the blocks. $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$.

The potential energy (in SI units) of a particle of mass $2 \mathrm{kg}$ in a conservative field is, $U=\left(6x- 8y\right) \mathrm{J}$. If the initial velocity of the particle is, $\overrightarrow{u}=\left(-1.5\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, then find the total distance ($\text{in} \mathrm{m}$) travelled by the particle in first two seconds.

Two blocks having masses $8 \mathrm{kg}$ and $16 \mathrm{kg}$ are connected to the two ends of a light spring. The system is placed on a smooth horizontal floor. An inextensible string also connects $B$ with ceiling as shown in the figure at the initial moment. Initially, the spring has its natural length. A constant horizontal force $F$ is applied to the heavier block as shown. What is the maximum possible value of $F \text{(in} \mathrm{N}\text{)}$ so the lighter block does not lose contact with ground.

A ring of mass $m=1\mathrm{kg}$ can slide over a smooth vertical rod. A light string attached to the ring passing over a smooth fixed pulley at a distance of $L=0.7 \mathrm{m}$ from the rod is shown in the figure. At the other end of the string, mass $M=5\mathrm{kg}$ is attached, lying over a smooth fixed inclined plane of inclination angle $37°$. The ring is held in level with the pulley and released. Determine the velocity of ring $\left(\mathrm{in} \mathrm{m} {\mathrm{s}}^{-1}\right)$ when the string makes an angle $\left(\alpha =37°\right)$ with the horizontal, $\left[\sin 37°=0.6\right]$