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 \[\mu \]. The acceleration a of the cart that will prevent the block from falling satisfies

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

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

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

D) \[\alpha <\frac{g}{\mu }\]

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 \[\mu R\ge mg\] \[\Rightarrow \]                               \[\mu \,m\alpha \,\ge mg\]        \[[as\,R\,=m\alpha ]\] \[\Rightarrow \]                               \[\alpha \ge \frac{g}{\mu }\]