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

Two uniform similar discs roll down two inclined planes of length $S$ and $2S$ respectively as shown is the fig. The velocities of two discs at the points $A$ and $B$ of the inclined planes are related as

One end of a straight uniform $1\; \mathrm{m}$ long bar is pivoted on horizontal table. It is released from rest when it makes an angle $30^{\circ}$ from the horizontal (see figure). Its angular speed when it hits the table is given as $\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},$ where $\mathrm{n}$ is an integer. The value of $n$ is

A circular disc of moment of inertia $I_t$, is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$ . Another disc of moment of inertia $l_b$ is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is 

A solid sphere rolls without slipping and presses a spring of spring constant $'k'$ as shown  in figure. Then, the compression in the spring will be :-