A large cubical shaped block of mass M rests on a fixed horizontal surface. Two blocks of mass $$m1$$ aod $$m2$$ are connected by a light inextensible string passing over a light pulley as shown. Neglect friction everyvhere. Then the constant horizontal force of magnitude F that should be applied to M so that $$m1$$ and $$m2$$ do not move relative to M is:

Question

A large cubical shaped block of mass M rests on a fixed horizontal surface. Two blocks of mass $$m1$$ aod $$m2$$ are connected by a light inextensible string passing over a light pulley as shown. Neglect friction everyvhere. Then the constant horizontal force of magnitude F that should be applied to M so that $$m1$$ and $$m2$$ do not move relative to M is:

Infinity Learn · Accepted Answer

Let a be the acceleration of cubical block of mass M from ground frame. Then from the frame of block of mass M, forces on $$m1$$ and $$m2$$ are as shown. Hence for $$m1$$ and $$m2$$ to remain at rest in frame of $$Mm2a$$ $$=$$ $$m1g$$ or a $$=$$ $$m1m2g$$∴  F $$=$$ $$m1m2(m1+m2+M)g$$

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