Embibe Experts Solutions for Exercise 4: Assignment

A uniform disc of mass $m$ and radius $R$ is pivoted at point $P$ and is free to rotate in vertical plane. The centre $C$ of disc is initially in horizontal position with $P$ as shown in figure. If it is released from this position, then its angular acceleration when the line $\mathrm{PC}$ is inclined to the horizontal at an angle $\theta$ is

A rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative

Consider a system of two particles having masses $m_1$ and $m_2.$ If the particle of mass $m_1$ is pushed towards $m_2$ through a distance $d,$ by what distance should be particle of mass $m_2$ be moved so as to keep the centre of mass of the system of particles at the original position ?

The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are

The $ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}$ and $I_{CA}$ are the moments of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct ?

Three particles, each of mass $m$ gram, are situated at the vertices of an equilateral triangle $ABC$ of side $I \mathrm{cm}$ (as shown in the figure). The moment of inertia of the system about a line $AX$ perpendicular to $AB$ and in the plane of $ABC,$ in ${\mathrm{gcm}}^2$ units will be

The reduced mass of two particles having masses $m$ and $2 m$ is

A point $P$ is the contact point of a wheel on ground which rolls on ground without slipping. The value of displacement of the point $P$ when wheel completes half of rotation (If wheel is $1 \mathrm{m}$ )