If unwrapped length of the thread between the cylinder and block $B$ is $20 m$ at the beginning, when the system was released from rest, what would it be 2s later?

28 m

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30 m

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22 m

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32.5 m

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Solution

The correct option is A $28 m$
Distance travelled by block B, $s_{B} = 0 + \frac{1}{2} a_{B} t^{2}$
$s_{B} = \frac{1}{2} \times 6 (2)^{2} = 12$ $m$
Thus length of the rop increases (due to block) by 12 m.
For cylinder: $a_{1} = r α - a = 4 \times 1 - 2 = 2$ $m / s^{2}$
Length of the rop decreases by $s^{'} = \frac{1}{2} a_{1} t^{2} = \frac{1}{2} \times 2 \times 2^{2} = 4$ $m$
Now net increase in length of rope $= 12 - 4 = 8$ $m$
Thus after 2 seconds, length of rop becomes 28 metres.

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