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A block of mass m is in contact with the cart C as shown. The coefficient of static friction between the block and cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies


\[(a)\;\alpha > mg/\mu \quad (b)\; \alpha >g/\mu\; m \quad (c)\; \alpha < g/ \mu \quad (d)\;\alpha \geq g/\mu \]

1 Answer

If the cart acceleration with $'\alpha \;'$
Pseudo force on mass $F=m \alpha$
Force of friction $=\mu N$
For horizontal equilibrium $F=N$
$f=\mu m \alpha$
The block will not fall as long as $ f \geq mg$
$\mu m \alpha \geq mg$
$\alpha \geq g/\mu$
Hence d is the correct answer.
answered Jul 10, 2013 by meena.p
edited May 27, 2014 by lmohan717

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