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A long block $A$ of mass $M$ is at rest on a smooth horizontal surface. A small block $B$ of mass $M$ / 2 is placed on $A$ at one end and projected along $A$ with some velocity $v$. The coefficient of friction between the block is $\mu$. Then, the accelerations of blocks $A$ and $B$ before reaching a common velocity will be respectively
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The correct answer is:
$\frac{\mu g}{2}$ (towards right), $\mu g$ (towards left)
The force causing the motion of $A$ is frictional force between $A$ and $B$,
So, acceleration of $A$
$\mu M_B g=M_A a_A$
$\Rightarrow a_A=\mu\left(\frac{M_B}{M_A}\right) g=\frac{\mu g}{2} \text { (towards right) }$
Block $B$ experiences frictions force toward left
$M_B a_B=\mu M_B g \Rightarrow a_B=\mu g \text { towards left }$
So, acceleration of $A$
$\mu M_B g=M_A a_A$
$\Rightarrow a_A=\mu\left(\frac{M_B}{M_A}\right) g=\frac{\mu g}{2} \text { (towards right) }$
Block $B$ experiences frictions force toward left
$M_B a_B=\mu M_B g \Rightarrow a_B=\mu g \text { towards left }$
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