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Question

A boy and a block, both of same mass m kg, are initially at the same horizontal level and attached to a frictionless pulley through a light inextensible string that moves over the frictionless pulley as shown in figure. The boy starts moving upward with an acceleration of 5 m/s2 relative to the rope. If the block has to travel a total distance of 10 m before reaching at the level of pulley, the time taken by the block in doing so is equal to


A
8 s
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B
22 s
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C
102 s
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D
8 s
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Solution

The correct option is B 22 s
FBD of the boy and the block is given below. Assume upward direction to be positive.


Acceleration of block w.r.t ground =am

Now, acceleration of boy w.r.t ground will be:

abg=abr+arg=abram=5am

For the boy,
Tmg=mabg=m×(5am) ..(1)

For mass m,
Tmg=mam ... (2)

From equations (1) and (2), we get am=52=2.5 m/s2

From the eqn Sy=uyt+12amt2,
Putting Sy=10 m and uy=0

t=2×10×25=22 s
Hence option (B) is correct.

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