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A system of two blocks of masses m=2 kg and M=8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be
[Take g=9.8 m s⁻²]

Asked in JEE Main 27th June 1st Shift 2022 · Friction between stacked blocks

Figure: Friction between stacked blocks
Answer: (3) 49 N

Step-by-step solution

Idea: friction between the blocks is the only thing accelerating the upper one, so it sets a ceiling on the shared acceleration. Turn that ceiling into a ceiling on F.

Upper block. The surfaces press together with N=mg, so the most friction available is

fₘₐₓ=μ mg=0.5×2×9.8=9.8 N.

That friction is all that drives the 2 kg block, so

aₘₐₓ=(fₘₐₓ)/m=(9.8)/2=4.9 m s⁻².

Note this is just μ g — the mass cancels.

Whole system. The table is smooth, so F alone accelerates M+m=10 kg:

Fₘₐₓ=(M+m)aₘₐₓ=10×4.9=49 N.

Push harder than that and the lower block slides out from under the upper one, which can never exceed μ g.

Why the other options are wrong

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