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Question

What horizontal force (in Newtons) must be applied to the cart as shown in figure, so that the blocks remain stationary relative to the cart? Assume all surfaces, wheels and pulley to be frictionless. (M=7 kg,m1=2 kg,m2=1 kg)

A
50
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B
55
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C
60
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D
40
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Solution

The correct option is A 50
Applying the newton's second law on whole system of two blocks+ pulley +string+cart:
(M=7 kg,m1=2 kg,m2=1 kg)
F=(M+m1+m2)a
a=F10, where a = acceleration of system.
Acceleration of both blocks are equal & equal to acceleration of cart, so that both blocks remain stationary with respect to the cart.

Now draw individual FBD including PSEUDO-FORCE

For block m1 to remain at stationary with respect to cart
T=m1a
Simillarly for second block, the condition to remain stationary w.r.t cart is:
T=m2g
m1a=m2g
m1F10=m2g
=2F10=10F=50 N

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