First slide

Rotational motion

Question

A rectangular block of mass M and height a is resting on a smooth level surface. A force F is applied to one corner as shown in the figure. At what point should a parallel
force 3F be applied in so that the block shall undergo pure translational motion? Assume normal contact force between the block and surface passes through the
center of gravity of the block.

Moderate

A

$\frac{a}{3} vertically above centre of gravity$
B

$\frac{a}{6} vertically above centre of gravity$
C

No such point exists
D

it is not possible

Solution

The free-body diagram of the block can be drawn as shown.
As the body has to move in pure translational motion, the torque about the center of gravity must be zero.
Torque of mg and N is zero as they are passing through COM.
Therefore, torque of 3F and F should balance each other.
$3 F \times x = F \times \frac{a}{2} \Rightarrow x = \frac{a}{6}$

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