2015 AIPMT-II System of Particles and Rotational MotionTorque and Angular Momentum Easy Question 2 of 2 in Torque and Angular Momentum

A force $\vec F = \alpha\hat i + 3\hat j + 6\hat k$ is acting at a point $\vec r = 2\hat i - 6\hat j - 12\hat k$. The value of $\alpha$ for which angular momentum about origin is conserved is:

A 1
B −1
C 2
D zero

The answer is B.

Solution

Angular momentum is conserved if $\vec\tau = \vec r\times\vec F = 0$, i.e. $\vec F \parallel \vec r$.
$\frac{\alpha}{2} = \frac{3}{-6} = \frac{6}{-12} \Rightarrow \alpha = -1$

Concept Zero torque condition

Torque and Angular Momentum in past papers

2 questions from this chapter have appeared across 2 exam years.