Question

A rought vertical board has an acceleration $a$, so that a $2\text{kg}$ block pressing against it does not fall. The coefficient of friction between the block and the board is $\mu$, then

• A. $\mu >\frac{a}{g}$
• B. $\mu <\frac{g}{a}$
• C. $\mu <\frac{a}{g}$
• D. $\mu >\frac{g}{a}$

Answer 1

The correct option is D $\mu >\frac{g}{a}$

By the free body diagram of the block,

The wall presses the block and so the reaction force towards left is $R$ and the pseudo force on the block will be towards right as $ma$

The frictional force $\left(f\right)$ here will prevent the block from falling

By the equilibrium condition, balancing the forces in vertical direction we get,

$f>mg$ , where $f=\mu R$
$\Rightarrow \mu \left(R\right)>mg$
$\Rightarrow \mu \left(ma\right)>mg$
$\Rightarrow \mu >\frac{g}{a}$

Hence, option D is the correct answer