First slide

Rolling motion

Question

A sphere has to purely roll upwards. At an instant when the velocity of sphere is v, frictional force acting on it is

Moderate

A

$downwards and μ m g \cos θ$
B

$downwards and \frac{2 m g \sin θ}{7}$
C

$upwards and μ m g \cos θ$
D

$upwards and \frac{2 m g \sin θ}{7}$

Solution

In case of rolling upwards in the inclined plane, let say friction acts upwards
Translation : $m g \sin θ - f = m a$
Rotation : $f R = (\frac{2}{5} m R^{2}) (\frac{a}{R})$
$For sphere, k^{2} = \frac{2}{5} R^{2}$
$From Eqs. (i) and (ii), f = \frac{2}{7} m g \sin θ (upwards)$

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