In shown figure m 1 = 2 kg and m 2 = 4 kg . The pulley is movable. At t = 0 , both masses touch the ground and the string is taut. A vertically upward, time dependent force F = 2 t ( F is in newto

Question

In shown figure m 1 ​ = 2 kg and m 2 ​ = 4 kg . The pulley is movable. At t = 0 , both masses touch the ground and the string is taut. A vertically upward, time dependent force F = 2 t ( F is in newton, t is in second) is applied to the pulley. (Take g = 10 ms − 2 ) List - I List - II (P) The time in seconds when m 1 ​ is lifted off the ground (1) 10 (Q) The time in seconds when m 2 ​ is lifted off the ground (2) 5 (R) Acceleration in m / s 2 ​ of m 1 ​ at t = 30 s (3) 20 (S) Acceleration in m / s 2 of m 2 ​ at t = 60 s (4) 40 (5) 30

TestHub · Accepted Answer

For the movable pulley, tension on each mass is $T = F /2 = t$ N.

(P) $m_{1}$ lifts when $T = 20$ N, so $t = 20$ s $\to$ (3)

(Q) $m_{2}$ lifts when $T = 40$ N, so $t = 40$ s $\to$ (4)

(R) At $t = 30$ s: $a_{1} = (30 - 20) /2 = 5 m/ s^{2}$ $\to$ (2)

(S) At $t = 60$ s: $a_{2} = (60 - 40) /4 = 5 m/ s^{2}$ $\to$ (2)

Answer: (A)

List - I	List - II
(P) The time in seconds when $m_{1}$ is lifted off the ground	(1) 10
(Q) The time in seconds when $m_{2}$ is lifted off the ground	(2) 5
(R) Acceleration in $m / s_{2}$ of $m_{1}$ at $t = 30 s$	(3) 20
(S) Acceleration in $m / s^{2}$ of $m_{2}$ at $t = 60 s$	(4) 40
	(5) 30

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