Question

A constant torque acting on a uniform wheel changes its angular momentum from A to 4A in 4 sec. The torque is:
$
  (a){\text{ }}\dfrac{{3A}}{4} \\
  (b){\text{ }}\dfrac{A}{4} \\
  (c){\text{ }}\dfrac{{2A}}{4} \\
  (d){\text{ }}\dfrac{{3A}}{2} \\
 $

Answer 1

Hint: In this question use the direct formula that torque acting upon the wheel will be $\dfrac{{{\text{change in angular momentum}}}}{{{\text{time taken by the circular wheel}}}}$, so compute the change in angular momentum and the time taken is given.

Complete step-by-step answer:
Given data:
Angular momentum changes from A to 4A.
So change in angular momentum = 4A – A = 3A.
Now it is given that the wheel takes 4 sec to change its angular momentum from A to 4A.
So the time (t) = 4s.
Now as we know that the torque acting on the circular wheel is the ratio of change in angular momentum to the time taken.
Therefore the torque acting on the circular wheel (T) = $\dfrac{{{\text{change in angular momentum}}}}{{{\text{time taken by the circular wheel}}}}$
$ \Rightarrow T = \dfrac{{3A}}{4}$
So this is the required constant torque working on the circular wheel.
Hence option (A) is the required answer.

Note:Torque can be viewed simply as a force responsible for rotation, it is also called twisting force, and angular momentum is essentially the product of the body's moment of inertia and the angular velocity of a body undergoing circular movement.