question_answer

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 p.. The acceleration a of the cart that will prevent the block from falling satisfies

A) \[a>\frac{mg}{\mu }\]

B) \[a>\frac{g}{\mu m}\]

C) \[a\ge \frac{g}{\mu }\]

D) \[a<\frac{g}{\mu }\] 

Correct Answer: C

Solution :

 When a cart moves with some acceleration toward right, then a pseudo force (ma) acts on block toward left. This force (ma) is action force by a block on cart. Now, block will remain static w.r.t. cart, if frictional force\[\mu R\ge mg\] \[\Rightarrow \]\[\mu ma\ge mg\] [as\[R=ma\]] \[\Rightarrow \]\[a\ge \frac{g}{\mu }\]