Question

A block of mass $m$ is in contact with the cart $C$ as shown in the figure.

The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies

• A. $\alpha >\frac{mg}{\mu }$
• B. $\alpha >\frac{g}{\mu m}$
• C. $\alpha \ge \frac{g}{\mu }$
• D. $\alpha <\frac{g}{\mu }$

Answer 1

Answer: (C)

Pseudo force or fictitious force, $F_{\text{fic }}=m\alpha$
Force of friction, $f=\mu N=\mu m\alpha$
The block of mass $m$ will not fall as long as
$f\ge mg$
$\mu m\alpha \ge mg$
$\alpha \ge \frac{g}{\mu }$