Embibe Experts Solutions for Chapter: Newton’s Laws of Motion, Exercise 1: Exercise 1

A point mass $m$ is suspended from a light thread of length $\mathcal{l},$ fixed at $O$, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:

A small object, suspended by a string, rotates with constant speed, in a horizontal circle as shown in the figure. Point $O$ is at the centre of the circle. Neglect air drag. Which one of the following statement is correct?

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of $30°$ with the ground. A monkey of mass $5 \mathrm{kg}$ climbs up the rope. The clamp can tolerate a vertical force of $40 \mathrm{N}$ only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take $g= 10 \mathrm{m} {\mathrm{s}}^{-2}$):

For the system shown in the figure, the acceleration of the mass $m_4$ immediately after the lower thread $x$ is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)

In figure shown, both blocks are released from rest. The time to cross each other is

Same spring is attached with $2 \mathrm{kg}, 3 \mathrm{kg}$ and $1 \mathrm{kg}$ blocks in three different case as shown in figure. If $x_1, x_2$ and $x_3$ be the extension in the spring in these three case then

A block $A$ of mass $m$ is placed over a plank $B$ of mass $2 \mathrm{m}$. Plank $B$ is placed over a smooth horizontal surface. The coefficient of friction between $A$ and $B$ is $0.5$. Block $A$ is given a velocity $v_0$ towards right. Acceleration of $B$ relative to $A$ is

A man of mass $50 \mathrm{kg}$ is pulling on a plank of mass $100 \mathrm{kg}$ kept on a smooth floor as shown with force of $100 \mathrm{N}$. both man & plank move together, find force of friction acting on man.