A triangular plate is shown. A force $\vec{F}=4 \hat{i}-3 \hat{j}$ is applied at point P. The torque at point P with respect to point 'O' and 'Q' are:

(B) $-15-20 \sqrt{3}, 15-20 \sqrt{3}$

(A) $15+20 \sqrt{3}, 15-20 \sqrt{3}$

(C) $-15+20 \sqrt{3}, 15+20 \sqrt{3}$

(D) $15-20 \sqrt{3}, 15+20 \sqrt{3}$

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Rotational Mechanics

A triangular plate is shown. A force

F = 4 \hat{i} - 3 \hat{j}

is applied at point P. The torque at point P with respect to point 'O' and 'Q' are:

Answer: (B)

Place

O

at the origin and

Q

(10, 0)

. The triangle is equilateral of side

10

, so

P

sits at

(5, 53)

.
About

O

the position vector of

P

r = 5 \hat{i} + 53 \hat{j}

, and for planar vectors

(a \hat{i} + b \hat{j}) \times (c \hat{i} + d \hat{j}) = (a d - b c) \hat{k}

τ_{O} = (5 \hat{i} + 53 \hat{j}) \times (4 \hat{i} - 3 \hat{j}) = (- 15 - 203) \hat{k}

About

Q

the position vector of

P

r = - 5 \hat{i} + 53 \hat{j}

τ_{Q} = (- 5 \hat{i} + 53 \hat{j}) \times (4 \hat{i} - 3 \hat{j}) = (15 - 203) \hat{k}

The torques about

O

and about

Q

are

- 15 - 203

and

15 - 203

respectively.

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option