A block of mass m is in contact with cart C as shown in figure. coefficient of static fric

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4-2.Friction

medium

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

(AIPMT-2010)

Solution

$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,\,pseudo\,force\,or\,fictitious\,force,\\
{F_{fic}} = m\alpha \,Force\,of\,friction,\,f = \mu N = \mu m\alpha \\
The\,block\,of\,mass\,m\\
will\,not\,fall\,as\,long\,\\
as\,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,f \ge mg\\
\,\,\,\,\,\,\,\,\,\,\mu m\alpha \ge mg\\
\,\,\,\,\,\,\,\,\,\,\,\,\alpha \ge \frac{g}{\mu }
\end{array}$

Standard 11

Physics

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