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The system starts from rest and A attains a velocity of $5 m / s$ after it has moved $5 m$ towards right. Assuming the arrangement to be frictionless every where and pulley & string to be light, the value of the force F applied on A is $(t a k e g = 10 m s^{- 2})$

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96 N

75 N

50 N

100 N

answer is B.

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Detailed Solution

Write constraint equation $\sum \vec{T} . \bar{a} = 0$

$\sum F = m a$

$F - 2 T = 6 a$ ............(1)

$T - 2 g = 2 (2 a)$ .......(2)

$5^{2} = 0^{2} + 2 a (5)$ .......(3)

After solving,

$a = 2.5 m s^{- 2}; T = 30 N; F = 75 N$

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