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A block of mass $\mathrm{m}$ is in contact with the cart $\mathrm{C}$ 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
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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
Solution:
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Verified Answer
The correct answer is:
$\alpha \geq \frac{g}{\mu}$
When a cart moves with some acceleration toward right then a pseudo force (ma) acts on block toward left. This force $(m \alpha)$ is action force by a block on cart Now, block will remain
static w.r.t. cart, if frictional force $\mu \mathrm{R} \geq \mathrm{mg}$
$$
\begin{array}{crrr}
\Rightarrow & \mu \mathrm{m} \alpha & \geq \mathrm{mg} & \text { [as } \mathrm{R}=\mathrm{m} \alpha \text { ] } \\
\Rightarrow & \alpha & \geq \frac{g}{\mu} &
\end{array}
$$
static w.r.t. cart, if frictional force $\mu \mathrm{R} \geq \mathrm{mg}$
$$
\begin{array}{crrr}
\Rightarrow & \mu \mathrm{m} \alpha & \geq \mathrm{mg} & \text { [as } \mathrm{R}=\mathrm{m} \alpha \text { ] } \\
\Rightarrow & \alpha & \geq \frac{g}{\mu} &
\end{array}
$$
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