Embibe Experts Solutions for Chapter: Motion of System of Particles and Rigid Body, Exercise 2: Level 2

A rod of length $L$ can rotate about end $0 .$ What is the work done if the rod is rotated by $180°$

A uniform rod of length $l$ and mass $m$ is free to rotate in a vertical plane about $A$. The rod initially in a horizontal position is released. The initial angular acceleration of the rod is (Moment of inertia of the rod about $A$ is $\frac{M{l}^2}{3}$)

Assertion : If the momentum of a particle is constant, then its angular momentum will also be constant

Reason : When net external force on an object is zero, then external torque on the object will also be zero.

A train is moving slowly at $2 \mathrm{m} {\mathrm{s}}^{-1}$ next to a railway platform. A man, $1.5 \mathrm{m}$ tall, alights from the train such that his feet are fixed on the ground. Taking him to be a rigid body, the instantaneous angular velocity (in $\mathrm{rad} {\mathrm{s}}^{-1}$) is

A solid homogeneous cylinder of height $h$ and base radius $r$ is kept vertically on a conveyer belt moving horizontally with an increasing velocity $v=a+b{t}^2.$ If the cylinder is not allowed to slip then the time when the cylinder is about to topple, will be equal to

A thin wire of length $\mathrm{L}$ and linear mass dếnsity $\rho$ is bent into a circular loop with centre at $\mathrm{O}$ as shown. The moment of inertia of the loop about the axis $XX$ ' is

A uniform square wooden sheet of side a has its centre of mass located at point $O$ as shown in the figure on the left. A square portion of side $b$ of this sheet is cut out to produce and $\mathrm{L}$-shaped sheet as shown in the figure on the right.

The centre of mass of the L-shaped sheet lies at the point $P$ (in the diagram) when,

Two uniform plates of the same thickness and area but of different materials, one shaped like an isosceles triangle and the other shaped like a rectangle are joined together to form a composite body as shown in the figure. If the centre of mass of the composite body is located at the midpoint of their common side, the ratio between masses of the triangle to that of the rectangle is,