The torque of a force $5 \hat{i}+3 \hat{j}-7 \hat{k}$ about the origin is $\tau$. If the force acts on a particle whose position vector is $2 \hat{i}+2 \hat{j}+\hat{k}$, then the value of $\tau$ will be :

(C) $-17 \hat{i}+19 \hat{j}-4 \hat{k}$

(A) $11 \hat{i}+19 \hat{j}-4 \hat{k}$

(B) $-11 \hat{i}+9 \hat{j}-16 \hat{k}$

(D) $17 \hat{i}+9 \hat{j}+16 \hat{k}$

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Rotational Mechanics

The torque of a force

5 \hat{i} + 3 \hat{j} - 7 \hat{k}

about the origin is

τ

. If the force acts on a particle whose position vector is

2 \hat{i} + 2 \hat{j} + \hat{k}

, then the value of

τ

will be :

(A) $11 \hat{i} + 19 \hat{j} - 4 \hat{k}$
(B) $- 11 \hat{i} + 9 \hat{j} - 16 \hat{k}$
(C) $- 17 \hat{i} + 19 \hat{j} - 4 \hat{k}$ ✓ Correct
(D) $17 \hat{i} + 9 \hat{j} + 16 \hat{k}$

Answer: (C)

Solution

Torque is given by

τ = r \times F

.

Using the determinant form:

τ = \hat{i} 25 \hat{j} 23 \hat{k} 1 - 7

Expanding:

= \hat{i} (2 \times (- 7) - 1 \times 3) - \hat{j} (2 \times (- 7) - 1 \times 5) + \hat{k} (2 \times 3 - 2 \times 5)

= \hat{i} (- 14 - 3) - \hat{j} (- 14 - 5) + \hat{k} (6 - 10)

= - 17 \hat{i} + 19 \hat{j} - 4 \hat{k}

The answer is (C).

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Single correct option

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