Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 1: KEAM 2020

The radius of gyration about an axis through the center of a hollow sphere with external radius $a$ and internal radius $b$ is

A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane, If the torque experienced by the hollow sphere and solid sphere are${\tau }_H$ and ${\tau }_S$ respectively, then

A uniform bar of mass $M$ is supported by a pivot at its top about which the bar can swing like a pendulum. If a force $F$ is applied perpendicular to the lower end of the bar as shown in figure, what is the value of $F$ in order to hold the bar in equilibrium at an angle $\left(\theta \right)$ from the vertical

A solid sphere of radius $\mathrm{r}$ is revolving about one of its diameters with an angular velocity $\mathrm{\omega }.$ If it suddenly expands uniformly so that its radius increases to $\mathrm{n}$ times its original value, then its angular velocity becomes

A thin circular ring of mass $m$ and radius $R$ is rotating about its axis perpendicular to the plane of the ring with a constant angular velocity $\omega$. Two point particles each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates, with an angular velocity $\frac{\omega }{2}$. Then, the ratio $\frac{m}{M}$ is

If a ring rolls down from top to bottom of an inclined plane, it takes time ${\mathrm{t}}_1.$ If it slides, it takes time ${\mathrm{t}}_2.$ Then the ratio $\frac{{\mathrm{t}}_2^2}{{\mathrm{t}}_1^2}$ is

A ball of mass $1 \mathrm{kg}$ and radius $0.5 \mathrm{m},$ starting from test rolls down on a $30°$ inclined plane. The torque acting on the ball at the distance of the $7 \mathrm{m}$ from the starting point is close to (take acceleration due to gravity as $10 \mathrm{m}/{\mathrm{s}}^2)$

If the radius of the earth suddenly decreases by half of its present value. Then the time duration of one day will be