A sphere of radius ‘a’ and mass ‘m’ rolls along a horizontal plane with constant speed v₀. It encounters and inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

Correct Option - 4


Detailed Solution:

Using conservation of energy between initial and final position shown :

$\left[\frac{1}{2}\left(\frac{2}{5}m{a}^2\right){\left(\frac{V_0}{a}\right)}^2+\frac{1}{2}m{V}_0^2\right]+0=mg\mathcal{l}sin\theta$

$\Rightarrow \frac{7}{10}m{V}_0^2=mg\mathcal{l}sin\theta$

$\Rightarrow \mathcal{l}=\frac{7v_0^2}{10gsin\theta }$

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