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A thin rod AB of length 2 m is bent at right angles at its mid point C and the bent rod rests on a smooth horizontal surface. When a force F is applied on the bent rod at point D as shown in the figure, the rod makes translational motion only. Then the length AD is

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65 cm

80 cm

50 cm

75 cm

answer is D.

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Detailed Solution

Line of action of the applied force F must pass through the centre of mass of the L-shaped rod

Now length $C D = \frac{(\frac{m}{2} \frac{l}{4} + \frac{m}{2} \times 0)}{(\frac{m}{2} + \frac{m}{2})} = \frac{l}{8}$

$∴ AD = \frac{l}{2} - \frac{l}{8} = \frac{3 l}{8} = \frac{3 \times 2}{8} m$

= 0.75 m

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