Embibe Experts Solutions for Chapter: Laws of Motion, Exercise 1: Level 1

Mass $m$ shown in figure is in equilibrium. If it is displaced further by $x$ and released find its acceleration just after it is released. Take pulleys to be light and smooth and strings light.

Same spring is attached with $2 \mathrm{kg},3 \mathrm{kg}$ and $1 \mathrm{kg}$ blocks in three different cases as shown in figure. If $x_1,x_2$ and $x_3$ be the extensions in the spring in these cases then (Assume all the blocks to move with uniform acceleration)

A light spring is compressed and placed horizontally between a vertical fixed wall and a block free to slide over a smooth horizontal table-top as shown in the figure. The system is released from rest. The graph which represents the relation between the magnitude of acceleration $a$ of the block and the distance  $x$ travelled by it (as long as the spring is compressed) is

A balloon is tied to a block. The mass of the block is $2 \mathrm{kg}$. The tension of the string between the balloon and the block is $30 \mathrm{N}$. Due to the wind, the string has an angle $\mathrm{\theta }$ relative to the vertical direction. $\mathrm{cos\theta }=\frac{4}{5}$ and $\mathrm{sin\theta }=\frac{3}{5}$. Assume the acceleration of gravity is $g=10 \mathrm{m} {\mathrm{s}}^{-2}$. Also assume the block is small so the force on the block from the wind can be ignored. Then the $x$ - component and the $y$-component of the acceleration of the block is

A particle of mass $m$ at rest is acted upon by a force $F$ for a time $t$. Its kinetic energy after an interval $t$ is

If $100 \mathrm{N}$ force is applied on the block. Then, frictional force acting on the block will be (in Newton),

Consider on a rough horizontal surface a block is kept. A horizontal force just strong enough to move the block is acting on it, the force is maintained for $2$ seconds and then removed. The total distance moved by the box is '$S$' meters. What is the value of '$6S$'?$\left({\mu }_s=0.2, {\mu }_k=0.15, g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A cyclist is moving with a speed of $6 \mathrm{m} {\mathrm{s}}^{-1}$. As he approaches a circular turn on the road of radius $120 \mathrm{m}$, he applies brakes and reduces his speed at a constant rate of $0.4 \mathrm{m} {\mathrm{s}}^{-2}$. The magnitude of the net acceleration of the cyclist on the circular turn just after brakes is