JEE Main 2025 Jan 22 Shift 2, Physics Q12: Angular Momentum, Its Conservation and Angular Impulse

JEE Main2025Jan 22, Shift 2Physics

The torque due to the force $(2 \hat{i} + \hat{j} + 2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i} + \hat{j} + \hat{k})$ , would be

A
$\hat{i} - \hat{j} + \hat{k}$
B
$\hat{i} + \hat{k}$
C
$\hat{i} - \hat{k}$
D
$\hat{j} - \hat{k}$

Solution

$τ = r \times F$ with $r = \hat{i} + \hat{j} + \hat{k}$ and $F = 2 \hat{i} + \hat{j} + 2 \hat{k}$ .

Using the determinant form:

$τ = \hat{i} \hat{j} \hat{k} 111212$

$= \hat{i} (1 \cdot 2 - 1 \cdot 1) - \hat{j} (1 \cdot 2 - 1 \cdot 2) + \hat{k} (1 \cdot 1 - 1 \cdot 2)$

$= \hat{i} (1) - \hat{j} (0) + \hat{k} (- 1) = \hat{i} - \hat{k}$ .

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JEE Main 2025 Jan 22 Shift 2, Physics Q12: Angular Momentum, Its Conservation and Angular Impulse

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