JEE Main202125 Feb 2021Evening ShiftPhysicsRotational MotionActual
A sphere of radius a and mass m rolls along a horizontal plane with constant speed v 0 . It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?
Options
- A2 5 v 0 2   g sin θ
- B7 v 0 2 10   g sin θ
- Cv 0 2 5 g sin θ
- Dv 0 2 2 g sin θ
Correct answer
B. 7 v 0 2 10   g sin θ
Step-by-step solution
From energy conservation mgh = 1 2 mv 0 2 + 1 2 Iω 2 ⇒ mgh = 1 2 mv 0 2 + 1 2 × 2 5 ma 2 × v 0 2 a 2 ⇒ gh = 1 2 v 0 2 + 1 5 v 0 2 ⇒ gh = 7 10 v 0 2 From triangle, sin   θ = h l Then h = l   sin   θ ⇒ l   sin   θ = 7 10 v 0 2   g Thus, the sphere will travel distance, l = 7 10 v 0 2   g   sin   θ .