JEE Main · 2006 · 30 Apr 2006 · Offline · Rotational Mechanics

A force of

- F \hat{k}

acts on O, the origin of the coordinate system. The torque about the point

(1, - 1)

(A) $- F (\hat{i} - \hat{j})$
(B) $F (\hat{i} - \hat{j})$
(C) $- F (\hat{i} + \hat{j})$ ✓ Correct
(D) $F (\hat{i} + \hat{j})$

Answer: (C)

Solution

The force

F = - F \hat{k}

acts at the origin, and the torque is taken about the point

(1, - 1, 0)

. The position of the origin relative to that point is

r = (0 - 1) \hat{i} + (0 - (- 1)) \hat{j} = - \hat{i} + \hat{j}

. Then

τ = r \times F = (- \hat{i} + \hat{j}) \times (- F \hat{k})

. Using

\hat{i} \times \hat{k} = - \hat{j}

and

\hat{j} \times \hat{k} = \hat{i}

, this works out to

- F \hat{i} - F \hat{j} = - F (\hat{i} + \hat{j})

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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