A triangular plate is shown. A force F = 4 i - 3 j is applied at… | JEE Main 2021 (17 Mar, Shift 1)

Q22JEE Main 2021 · 17 MAR · SHIFT 1Medium

Torque, Couple & Equilibrium of Rigid Bodies

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:

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Answer: (d)

From the figure: O = (0,0), Q = (10,0), P = $(10\cos 60^\circ, 10\sin 60^\circ) = (5, 5\sqrt{3})$ cm; $\vec{F} = 4\hat{i}-3\hat{j}$ .
Planar torque: $\tau_z = xF_y - yF_x$ .
About O: $\tau = 5(-3) - 5\sqrt{3}(4) = -15 - 20\sqrt{3}$
About Q: $\vec{r} = (-5, 5\sqrt{3})$ , $\tau = (-5)(-3) - 5\sqrt{3}(4) = 15 - 20\sqrt{3}$
So the answer is (d).

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