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Question

# A frictionless cart of mass M carries two other frictionless carts having masses m1 and m2 connected by a string passing over a pulley as shown in figure. The horizontal force that must be applied on M, so that m1 and m2 do not move relative to it will be

A
(M+m1+m2)(m2m1)g
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B
(M+m1+m2)(m1m2)g
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C
(M+m1)[(m1+m2)m2]g
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D
(M+m2)[m2(m1+m2)]g
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Solution

## The correct option is A (M+m1+m2)(m2m1)g F=(M+m1+m2)a a=F(M+m1+m2) pseudo force on m1, F′=m1a=m1F(M+m1+m2)=T....(i) For m2,T=m2g....(ii) from (i) & (ii) F′=m2g m1F(M+m1+m2)=m2g ∵F=m2gm1(M+m1+m2) ∵F=m2gm1(M+m1+m2) So option (A) is correct.

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