Laws of Motion - Result Question 44
44. A block of mass $m$ is in contact with the cart $C$ as shown in the Figure.
[2010]
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) $\alpha>\frac{m g}{\mu}$
(b) $\alpha>\frac{g}{\mu m}$
(c) $\alpha \geq \frac{g}{\mu}$
(d) $\alpha<\frac{g}{\mu}$
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Answer:
Correct Answer: 44. (c)
Solution:
- (c) Forces acting on the block are as shown in the fig. Normal reaction $N$ is provided by the force ma due to acceleration $\alpha$
$\therefore \quad N=ma$ For the block not to fall, frictional force, $F_f \geq mg$
$\Rightarrow \mu N \geq mg$
$\Rightarrow \mu ma \geq mg$
$\Rightarrow a \geq g / \mu$
When a cart moves with some acceleration towards right then a psendo force (ma) acts on block towards left. This force ma is action force by a block on cart.
