A wheel of radius $20\, cm$ has forces applied to it as shown in the figure. The net torque produced by the forces $4\, N$ at $A, 8\, N$ at $B, 6\, N$ at $C$ and $9\, N$ at $D$ at angles indicated is

A particle originally at rest at the highest point of $a$ smooth vertical circle is slightly displaced. It will leave the circle at $a$ vertical distance $h$ below the highest point, such that

The centre of mass of two masses $m$ and $m'$ moves by distance $\frac {x}{5}$ when mass $m$ is moved by distance $x$ and $m'$ is kept fixed. The ratio $\frac {m'}{m}$ is

The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta (t) = 2t^3 -6t^2$. The torque on the wheel becomes zero at $t$ $=$ ........ $\sec.$

A plank is moving in a horizontal direction with a constant acceleration $\alpha \hat{ i }$. A uniform rough cubical block of side $l$ rests on the plank and is at rest relative to the plank. Let the centre of mass of the block be at $(0, l / 2)$ at a given instant. If $\alpha =g / 10$, then the normal reaction exerted by the plank on the block at that instant acts at

A ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without  rolling. It gradually picks up rotation motion. Find the speed of the ball at which there will  be rolling without slipping-