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Question

Block A of weight 500 N and block B of weight 700 N are connected by rope pulley system as shown in the figure. The largest weight C in N that can be suspended without moving block A and B in Newton is (The coefficient of friction for all plane surfaces of contact is 0.3. The pulleys are ideal.):

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A
810
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B
90
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C
270
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D
900
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Solution

The correct option is B 810
From FBD of block A, T=f=μ(mAg)=500μ=500×0.3=150N ...(1),
where given weight of A is mAg=500N
Now for block B:
f+(T+2T)+f=T+f
3T+μ(mAg+mBg)=T
3T+0.3×(500+700)=T
3T+360=T ...(2)
For block C:
T=W ....(3) where W= weight of block C such that blocks A and B will not move.
Using (1), (2) and (3), W=450+360=810N

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