Question

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

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

Answer 1

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

The FBD of the block is shown below in the board frame of reference.


From the FBD, we get
$N=ma$ and
$f=\mu N=\mu ma$ (in limiting case)
If block does not fall, it means
$f>mg$
$\Rightarrow \mu \left(ma\right)>mg$
$\Rightarrow \mu >\frac{g}{a}$