H C Verma Solutions for Chapter: Newton's Laws of Motion, Exercise 4: EXERCISES

Two blocks of equal mass $m$ are tied to each other through a light string and placed on a smooth horizontal table. One of the blocks is pulled along the line joining them with a constant force $F$. Find the tension in the string joining the blocks.

A monkey of mass $15 \mathrm{kg}$ is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$, how much force should it apply to the rope? If the rope is $5 \mathrm{m}$ long and the monkey starts from rest, how much time will it take to reach the ceiling?

A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end as shown in the figure given below. Show that, whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially, both were at rest, their separation will not change as time passes.

The monkey $B$shown in figure given below is holding on to the tail of the monkey $A$which is climbing up a rope. The masses of the monkeys $A$and $B$are $5 \mathrm{kg}$and $2 \mathrm{kg},$respectively. If monkey $A$can tolerate a tension of $30 \mathrm{N}$in its tail, what force should it apply on the rope in order to carry the monkey $B$with it? Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Figure given below shows a man of mass $60 \mathrm{kg}$standing on a light weighing machine kept in a box of mass $30 \mathrm{kg}$. The box is hanging from a pulley fixed to the ceiling through a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, what is the weight shown by the machine? What force should he exert on the rope to get his correct weight on the machine?

A block $A$ can slide on a frictionless incline of an angle $\mathrm{\theta }$and length $l,$kept inside an elevator going up with a uniform velocity $v$ (see figure). Find the time taken by the block to slide down the length of the incline, if it is released from the top of the incline.

A car is speeding up on a horizontal road with an acceleration $a.$ Consider the following situations in the car.

(a) A ball is suspended from the ceiling through a string and is maintaining a constant angle with the vertical. Find this angle.

(b) A block is kept on a smooth incline and does not slip on the incline. Find the angle of the incline with the horizontal.

A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of $12 \mathrm{m} {\mathrm{s}}^{-2}$. Find the displacement of the block during the first $0.2 \mathrm{s}$ after the start. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.