A solid sphere is rolling on a surface as shown in figure, with a translational velocity v ms-1. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

Question

A solid sphere is rolling on a surface as shown in figure, with a translational velocity v ms-1. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is (A) √2gh (B) √(7/5)gh (C) √(7/2)gh (D) √(10/7)gh

Tardigrade Admin · Accepted Answer

Minimum velocity fin- a body rolling without slipping v = √(2gh/1+(K2)R2) For solid sphere, (K2/R2) = (2/5) ∴ v = √(2gh/1+(K2)R2) = √(10/7)gh

Q. A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v m s^{- 1}$ . If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

$2 g h$

$\frac{7}{5} g h$

$\frac{7}{2} g h$

$\frac{10}{7} g h$

Minimum velocity fin- a body rolling without slipping
$v = \frac{2 g h}{1 + \frac{K ^{2}}{R ^{2}}}$
For solid sphere, $\frac{K ^{2}}{R ^{2}} = \frac{2}{5}$
$∴ v = \frac{2 g h}{1 + \frac{K ^{2}}{R ^{2}}} = \frac{10}{7} g h$

Q. A solid sphere is rolling on a surface as shown in figure, with a translational velocity vms−1. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

2gh​

57​gh​

27​gh​

710​gh​