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 y. The acceleration a of the cart that will prevent the block from falling satisfies [AIPMT (S) 2010] |
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 \[\mu R\ge mg\] |
\[\Rightarrow \] \[\mu \,m\alpha \,\ge mg\] \[[as\,R\,=m\alpha ]\] |
\[\Rightarrow \] \[\alpha \ge \frac{g}{\mu }\] |
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