$A$ string is wound around the rim of a mounted flywheel (disc) of mass $20 \, kg$ and radius $20 \, cm$. $A$ steady pull of $25 \, N$ is applied on the cord. Neglecting friction and the mass of the string,the angular acceleration of the wheel in $rad/s^2$ is

At time $t = 0$,a $2\, kg$ particle has position vector $\vec{r} = (4\hat{i} - 2\hat{j})\, m$ relative to the origin. Its velocity is given by $\vec{v} = 2t^2\hat{i}\, m/s$. The torque acting on the particle about the origin at $t = 2\, s$ is ........ $\hat{k}\, N\cdot m$.

The moment of inertia of a wheel about its transverse axis is $2 \ kg \cdot m^2$ and it is rotating at $60 \ rpm$ about that axis. The torque required to stop the wheel in one minute is:

$A$ wheel has a moment of inertia $5 \times 10^{-3} \, kg \, m^2$ and is making $20 \, rev/sec$. The torque needed to stop it in $10 \, sec$ is $............. \times 10^{-2} \, N-m$. (in $\pi$)

$A$ rectangular plate of mass $20 \ kg$ is suspended from points $A$ and $B$ as shown in the figure. If the pin at $B$ is suddenly removed,find the angular acceleration of the plate in $rad/s^2$.

An automobile moves on a road with a speed of $54 \,km h^{-1}.$ The radius of its wheels is $0.45\, m$ and the moment of inertia of the wheel about its axis of rotation is $3\, kg m^2$. If the vehicle is brought to rest in $15\, s,$ the magnitude of average torque transmitted by its brakes to the wheel is .......... $kg \,m^2\, s^{-2}$.