Two equal-magnitude forces act at the same point from a door hinge

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two equal-magnitude forces act at the same point

0.8\,\text{m}

from a door hinge. Force

P

is applied at

90^{\circ}

to the door, while force

Q

is applied at

30^{\circ}

to the door surface. Which relation between their torque magnitudes

\tau_P

and

\tau_Q

is correct? (a)

\displaystyle \tau_P = \dfrac{1}{2}\,\tau_Q

(b)

\displaystyle \tau_P = \sqrt{3}\,\tau_Q

(c)

\displaystyle \tau_P = 2\,\tau_Q

(d)

\displaystyle \tau_P = \dfrac{2}{\sqrt{3}}\,\tau_Q