Assertion (A): For a system of particles under central force field, the total angular momentum is conserved.
Reason (R): The torque acting on such a system is zero.
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false
Solution:
Assertion (A) is true, angular momentum is conserved when net torque is zero. Reason (R) is true. For a central force \(vec{F}\) acting along \(vec{r}\) (position vector), the torque \(vec{tau} = vec{r} times vec{F} = 0\). Since \(vec{tau}=0\), \(frac{text{d}vec{text{L}}}{text{dt}} = 0\), hence \(vec{text{L}}\) is conserved. (R) correctly explains (A).
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