Question

Under constant torque, the angular momentum of a body changes from A to 4A in 4s. The torque is:
A. $3A$
B. $\dfrac{A}{3}$
C. $\dfrac{3A}{4}$
D. $\dfrac{4A}{3}$

Answer 1

The rate of change in angular momentum about the rotational axis of the body is defined to be the torque applied on it. For a constant torque, the ratio of the change in angular momentum of the body in some time interval is equal to the applied torque.

Formula used:
$\tau =\dfrac{\Delta L}{\Delta t}$
where $\tau$ is constant torque and $\Delta L$ is the change in angular momentum in time $\Delta t$.

Complete step by step answer:
When we talk about the rotational motion of a body, we say that the body accelerates rotationally when a torque is applied to it. Let us understand what torque applied on a body is. When a torque is applied on a body about some rotational axis, the angular momentum of the body about that axis changes. The rate of change in angular momentum about the rotational axis of the body is defined to be the torque applied on it.For a constant torque, the ratio of the change in angular momentum of the body in some time interval is equal to the applied torque.
i.e. $\tau =\dfrac{\Delta L}{\Delta t}$ ….. (i)
It is given that the angular momentum of the given body changes from A to 4A in a time interval of 4s.
This means that $\Delta L=4A-A=3A$ and $\Delta t=4s$.
Substitute these values in equation (i).
$\therefore \tau =\dfrac{3A}{4}$.
This means that the value of torque applied on the body is equal to $\dfrac{3A}{4}$.

Hence, the correct option is C.

Note: If it is difficult to understand torque then you can relate it to a force. Torque is said to be analogous to force and angular momentum is analogous to linear momentum. Similar to torque, the rate of change in linear momentum of a body is equal to the force applied on it.