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
$f \geq m g$
$\mu m \alpha \geq m g $
$\alpha \geq \frac{g}{\mu}$