$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration is $10 \,rad \,s^{-2}$. The tangential force applied to the rim of the disc is (in $\,N$)

$A$ rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis (see figure). When released from the initial horizontal position,its instantaneous angular acceleration will be

$A$ rope is wound around a solid cylinder of mass $1 \,kg$ and radius $0.4 \,m$. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $25 \,N$? (The cylinder is rotating about its own axis.)

$A$ flywheel of moment of inertia $0.4 \, kg \, m^2$ and radius $0.2 \, m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10 \, N$,then the angular velocity after $4 \, s$ will be ......... $rad \, s^{-1}$.

$A$ flywheel of moment of inertia $2 \, kg \cdot m^2$ is rotated at a speed of $30 \, rad/s$. $A$ tangential force at the rim stops the wheel in $15 \, s$. The average torque of the force is ........... $N \cdot m$.

$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $L_0$ to $4L_0$ in $4 \ s$. The magnitude of this torque is