Question

A block of mass $m$ is in contact with the cart $\text{C}$ as shown in 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. $\alpha <\frac{g}{\mu }$
• B. $\alpha >\frac{mg}{\mu }$
• C. $\alpha \ge \frac{g}{\mu }$
• D. $\alpha >\frac{g}{\mu m}$

Answer 1

The correct option is C $\alpha \ge \frac{g}{\mu }$

From FBD:


Here, $f=mg\text{and}N=m\alpha$

But $f\le \mu N$

So, using above equations,

$mg\le \mu m\alpha$

$\Rightarrow \alpha \ge \frac{g}{\mu }$

Hence, $\left(C\right)$ is the correct answer.