Rotational kinetic energy of a given body about an axis is proportional to

A disc of mass $1\,kg$ and radius $R$ is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $4 \sqrt{\frac{x}{3 R}}$ rad s$^{-1}$ where $x=$

$\left( g =10\,ms ^{-2}\right)$

Part of the tuning arrangement of a radio consists of a wheel which is acted on by two parallel constant forces as shown in the fig. If the wheel rotates just once, the work done will be about (diameter of the wheel = $0.05\ m$)

A student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above ground when standing straight. She wants to jump up vertically. To do so. she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force F. As a result, she jumps up such that the maximum height of her feet is $0.3 \,m$ above ground. The ratio $F / Mg$ is

A circular disc is rolling on a horizontal plane. Its total kinetic energy is  $300\,\,J.$  ......... $J$ is its translational  $K.E.$

Three particles are situated on a light and rigid rod along $Y$axis as shown in the figure. If the system is rotating with an angular velocity of $2\,rad/\sec $about $X$axis, then the total kinetic energy of the system is ...... $J$