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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:

Option 1)
$\alpha > \frac{mg}{\mu }$

Option 2)
$\alpha > \frac{g}{\mu m}$

Option 3)
$\alpha \geq \frac{g}{\mu }$

Option 4)
$\alpha < \frac{g}{\mu }$

Answers (1)

As we learnt in

Sticking of block with accelerated cart -

For equilibrium condition

$mu mageq mg$

$ageq frac{g}{mu}$

R = ma

$herefore ; a_{min}=frac{g}{mu}$

$F_{min}=(M+m)frac{g}{mu}$

- wherein

Pseudo force (ma) acts on block towards left

F_min = Minimum forc

a_min = minimum accleration cart

M, m are masses of cart and block respectively

$Mg=$ $Mg= g_{f}r------(i)$

$N=F_{p}=m \propto-------(ii)$

$Mg = \mu N$ => $Mg = \mu m \propto$

$\propto\:\geq \frac{g}{\mu }$

Option 1)

$\alpha > \frac{mg}{\mu }$

This option is incorrect.

Option 2)

$\alpha > \frac{g}{\mu m}$

This option is incorrect.

Option 3)

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

This option is correct.

Option 4)

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

This option is incorrect.

Posted by

Vakul

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