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Question

Find the value of acceleration of block B (in m/s2) for the system shown in figure. Take g=10 m/s2.


A
152 m/s2
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B
52 m/s2
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C
8 m/s2
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D
252 m/s2
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Solution

The correct option is A 152 m/s2
Total length of string (l) will remain constant. Let the length of the string between block B and pulley attached to block A be xA.


l=xB+3xA ...(i)
where l represents total string length at the level of the pulley attached to A.
Differentiating Eq (i) twice w.r.t time,
0=d2xBdt2+3d2xAdt2
0=aB+3aA
(aB is ve since distance xB is decreasing)
aB=3aA ...(ii)

Applying Newton's 2nd law for block B,
T=maB....(iii)
For block A,
3mg3T=3maA
or mgT=maA ...(iv)

From Eq. (ii), (iii), (iv):
mg=maA+maB
mg=4maA
aA=104=52 m/s2
& aB=152 m/s2

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