$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

Which of the following are correct expressions for torque acting on a body?
$A. \ \vec{\tau}=\vec{ r } \times \vec{ L }$
$B. \ \vec{\tau}=\frac{ d }{ dt }(\vec{ r } \times \vec{ p })$
$C. \ \vec{\tau}=\vec{ r } \times \frac{ d \vec{ p }}{ dt }$
$D. \ \vec{\tau}= I \vec{\alpha}$
$E. \ \vec{\tau}=\vec{ r } \times \vec{ F }$
($\vec{ r }=$ position vector; $\vec{ p }=$ linear momentum;
$\vec{ L }=$ angular momentum; $\vec{\alpha}=$ angular acceleration;
$I=$ moment of inertia; $\vec{ F }=$ force; $t =$ time)
Choose the correct answer from the options given below:

Which of the following relations is incorrect?

What does the time rate of change of angular momentum represent?

If a force acts on a body at a point away from the center of mass,then:

$A$ 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