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A T-shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $\vec{F}$ is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

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$ℓ$

$\frac{2 ℓ}{3}$

$\frac{3 ℓ}{4}$

$\frac{4 ℓ}{3}$

answer is A.

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Detailed Solution

P must be applied at centre of mass.

The distance ‘r’ of the centre of mass of the system from the point C is given by,

$r = \frac{m_{1} r_{1} + m_{2} r_{2}}{m_{1} + m_{2}} \Rightarrow r = \frac{m \times 2 ℓ + 2 m \times ℓ}{m + 2 m} \Rightarrow r = \frac{4 ℓ}{3}$

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