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

• A

  $\alpha>\frac{m g}{\mu}$
• B

  $\alpha>\frac{g}{\mu \mathrm{m}}$
• Correct answer
  C

  $\alpha \geq \frac{g}{\mu}$
• D

  $\alpha < \frac{g}{\mu}$

Solution

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 $\mu \mathrm{R} \geq \mathrm{mg}$ $$ \begin{array}{crrr} \Rightarrow & \mu \mathrm{m} \alpha & \geq \mathrm{mg} & \text { [as } \mathrm{R}=\mathrm{m} \alpha \text { ] } \\ \Rightarrow & \alpha & \geq \frac{g}{\mu} & \end{array} $$

Hence, the correct answer is option: 'C'.