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Direction of Friction

A single hori...

Question

A single horizontal force F is applied to a block of mass $M_{1}$ ,which is in contact with another block of mass $M_{2}$ (Fig. 3.2). If the surfaces are frictionless, the force between the blocks is

\frac{M_{1} F}{M_{2}}

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\frac{M_{1} M_{2} g}{M_{1} + M_{2}}

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\frac{M_{2} F}{M_{1} + M_{2}}

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None of these

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Solution

The correct option is C $\frac{M_{2} F}{M_{1} + M_{2}}$
Both block are moving with same acceleration $a$ .
$F = (M_{1} + M_{2}) a$ ,
$\Rightarrow a = \frac{F}{M_{1} + M_{2}}$ ,
Let $N$ is force between the blocks,
From FBD of block $M_{2}$ ,
$N = M_{2} \times a$
$\Rightarrow N = \frac{M_{2} F}{M_{1} + M_{2}}$

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