First slide

Rotational motion

Question

Two blocks each of the mass m are attached to the ends of a massless rod which pivots as shown in the figure. Initially, the rod is held in the horizontal position and then released. Calculate the net torque on this system above pivot.

Easy

A

$(m l_{2} g - m l_{1} g) \hat{k}$
B

$(m l_{1} g - m l_{2} g) \hat{k}$
C

$(m l_{1} g + m l_{2} g) \hat{k}$
D

$- (m l_{1} g + m l_{2} g) \hat{k}$

Solution

Torque due to the weight of Left m:
${\vec{τ}}_{1} = m g l_{1} \hat{k} (∴ this is anti-clock wise)$
Torque due to weight of right m:
${\vec{τ}}_{2} = - m g l_{2} \hat{k} (∴ this is clockwise)$
$So net torque: \vec{τ} = {\vec{τ}}_{1} + {\vec{τ}}_{2} = (m g l_{1} - m g l_{2}) \hat{k}$

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