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
AIPMT 2010, Medium
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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
$f \geq m g$
$\mu m \alpha \geq m g$
$\alpha \geq \frac{g}{\mu}$
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