JEE Main 2025 Apr 4 Shift 1, Physics Q4: Angular Momentum, Its Conservation and Angular Impulse

JEE Main2025Apr 4, Shift 1Physics

Which of the following are correct expression for torque acting on a body?

A. $τ = r \times L$

B. $τ = \frac{d}{d t} (r \times p)$

C. $τ = r \times \frac{d p}{d t}$

D. $τ = I α$

E. $τ = r \times F$

( $r$ = position vector; $p$ = linear momentum; $L$ = angular momentum; $α$ = angular acceleration; $I$ = moment of inertia; $F$ = force; $t$ = time)

Choose the correct answer from the options given below :

A
B, D and E Only
B
C and D Only
C
B, C, D and E Only
D
A, B, D and E Only

Solution

Torque is the time rate of change of angular momentum $L = r \times p$ . So $τ = \frac{d L}{d t} = \frac{d}{d t} (r \times p)$ — option B is correct.

Expanding the derivative: $\frac{d}{d t} (r \times p) = \frac{d r}{d t} \times p + r \times \frac{d p}{d t}$ . The first term is $v \times m v = 0$ , leaving $τ = r \times \frac{d p}{d t}$ — option C is correct.

Using Newton's second law $\frac{d p}{d t} = F$ gives $τ = r \times F$ — option E is correct.

For a rigid body about a fixed axis, $τ = I α$ — option D is correct.

Option A ( $τ = r \times L$ ) is dimensionally and physically wrong.

$∴$ Correct expressions are B, C, D and E.

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JEE Main 2025 Apr 4 Shift 1, Physics Q4: Angular Momentum, Its Conservation and Angular Impulse

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