A single horizontal force $F$ is applied to a block of mass $M$ , which is in contact with another block of mass $M$ . 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 $\frac{M_{2} F}{M_{1} + M_{2}}$
consider them as a combined mass then :

$F = (M_{1} + M_{2}) . a$

$a = \frac{F}{(M_{1} + M_{2})}$ ………………Eqn 1

the force equations for both blocks.

Block $M_{1}$ :

$F - F_{1} = M_{1} . a$ ……………Eqn2

Block $M_{2} :$

$F_{1} = M_{2} . a$ …………….Eqn3

for $“ F_{1} ”$ .

You can use Eqn 2 or Eqn 3 and substitute for “a” using Eqn 1.

Let us take Eqn 3 since it is simple.

$F_{1} = M_{2} . a = \frac{M_{2} . F}{(M_{1} + M_{2})}$

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A single horizontal force F is applied to a block of mass M, which is in contact with another block of mass M. If the surfaces are frictionless, the force between the blocks is

A single horizontal force $F$ is applied to a block of mass $M$ , which is in contact with another block of mass $M$ . If the surfaces are frictionless, the force between the blocks is