Question

A particle of mass M is released in vertical plane from a point P at $x$ = $x_0$ on the axis it falls vertically

along the y-axis. Find the torque $\tau$ acting on the particle at a time t about origin?

• A. $mg{x}_0\hat{k}$
• B. $-mg{x}_0\hat{k}$
• C. $2mg{x}_0\hat{k}$
• D. $3mg{x}_0\hat{k}$

Answer 1

The correct option is A

$mg{x}_0\hat{k}$

Torque is produced by the force of gravity.
$\overrightarrow{\tau }=rFsin\theta \hat{k}$ or
As r sin θ =$x_0$
As r_⊥ F
$|\overrightarrow{\tau }|=x_{0}mg$
$\overrightarrow{\tau }=mg{x}_0\hat{k}$