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A thin uniform thin rod AB of mass m and length L is lying on a frictionless table. A particle of mass m is attached to the end B. A horizontal force F is applied to the rod at point P. If the rod performs pure translational motion, the length AP is

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$\frac{l}{3}$

$\frac{l}{4}$

$\frac{2 l}{3}$

$\frac{3 l}{4}$

answer is D.

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Detailed Solution

For pure translational motion, point P must be the position of centre of mass of rod-particle system.

Taking origin at A the C.M. of system lies at

$∴ A P = \frac{m \times \frac{l}{2} + m \times l}{m + m} = \frac{3 l}{4}$

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