Question

A bolt is being tightened by a $20N$ force applied to a $25cm$ long wrench at an angle of ${60}^{\circ }$ with the wrench. The magnitude of the torque is

• A. $100\sqrt{3}$
• B. $500\sqrt{3}$
• C. $250\sqrt{3}$
• D. $250$

Answer 1

The correct option is C $250\sqrt{3}$

Let the position vector be $r$ and the force vector be $F$.

Then the torque acting on position vector by the force is defined as $T=r\times F$.

here $|r|=25cm$ and $|F|=20N$.

so torque $T=|r||F|sin\theta$ (where $\theta$ is angle between them)

$T=20\times 25\times sin\left(60\right)$

$T=250\sqrt{3}$.