Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 1: AP EAPCET Medical 2018 (22-Apr Shift-1)

A wheel of mass $10 \mathrm{kg}$ has moment of inertia equal to $0.1 \mathrm{kg} {\mathrm{m}}^2.$ Then its radius of gyration equals $\underline{ }$

Four spheres each of radius $0.05 \mathrm{m}$ and mass $1 \mathrm{kg}$ are placed one at each corner of a square of side $0.2 \mathrm{m},$ such that their centres coincide with the corners of the square. Find the moment of inertia of the system about one side of the square.

A constant torque acting on a uniform circular wheel changes its angular momentum from $1A_0$ to $5A_0$ to in $6$ seconds. Then the magnitude of torque is____________

A rigid solid sphere is spinning around an axis without any external torque. Due to change in temperature, its volume increases by $1\%$. Then its angular speed________

If the radius of a spherical object, rotating about its diameter with a time period of $2$ seconds, is reduced to half its actual value, keeping its mass unchanged, its time period becomes ________
(assuming zero external torque)

The kinetic energy of a rolling ring of mass $0.3 \mathrm{kg}$ about an axis passing through its centre of mass and perpendicular to its plane, if its centre of mass is moving with a velocity of $8 \mathrm{m} {\mathrm{s}}^{-1}$ is_________

A wheel of mass $10 \mathrm{kg}$ and radius of gyration $50 \mathrm{cm}$ is rotating at $300 \mathrm{rpm}.$ The rotational kinetic energy of the wheel is

A solid cylinder of mass $\text{'}m\text{'}$ and radius $\text{'}r\text{'}$ starts rolling down an inclined plane of inclination $\theta .$If the friction is just enough to prevent slipping. the speed of its centre of mass after it has descended through a height $\text{'}h\text{'}$ is given by