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

A plank is rotating in a vertical plane about one of its ends with a constant angular velocity $\omega =\sqrt{2}$ rad/s. A block of mass m = 2 kg is placed at a distance I = 1m from its end A (see diagram) which is hinged. The block starts sliding down when the plank makes an angle $\theta =30^{\circ }$ with the horizontal. If coefficient of friction between the plank and the block is $\mu$ and given that ${\mu }^2=\text{k/25}$. The value of k is

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration $a$ directed horizontally as shown in figure. The other end of the string is pulled with constant acceleration $a$ (relative to car) vertically. The tension in the string is equal to,

A body of mass $5 \mathrm{kg}$ at rest explodes and breaks into three pieces of masses in the ratio $1:1:3$. The first two pieces fly off perpendicular to each other with a speed of $30 {\mathrm{ms}}^{-1}$ each. The velocity of the heavier piece is,

Statement I : If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.

Statement II : The linear momentum of an isolated system remains constant.

Select the correct option.

Two spheres of masses $2 M$ and $M$ are initially at rest at a distance $R$ apart. Due to mutual force of attraction, they approach each other. When they are at separation $\frac{R}{2}$ the acceleration of the centre of mass of sphere would be [in SI units]:-

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 plank is rotating in a vertical plane about one of its fixed end $\mathrm{A}$ with a constant angular velocity $\omega =\sqrt{2} \mathrm{rad} {\mathrm{s}}^{-1}.$ A block of mass $\mathrm{m}=2 \mathrm{kg}$ is placed at a distance $l=1 \mathrm{m}$ from end $\mathrm{A}$ (see figure) which is hinged. The block starts sliding down when the plank makes an angle $\theta =30°$ with the horizontal. If coefficient of friction between the plank and the block is $\mu$ and given that ${\mu }^2=\frac{k}{25}$. Find the value of $k$.