A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be _________ cm (take, g = 10 m s⁻²) Image
Physics · Circular Motion
JEE Mains 8 April 2023 Shift 2 Evening Shift

Question

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be _________ cm (take, g = 10 m s⁻²) Image

Physics · Circular Motion

JEE Mains 8 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

For a hollow spherical ball, I = (2/3)MR² For pure rolling, ω = v/R Initial total kinetic energy: K = (1/2)Mv² + (1/2)Iω² = (1/2)Mv² + (1/2)(2/3 MR²)(v²/R²) = (1/2 + 1/3)Mv² = (5/6)Mv² At maximum height all kinetic energy converts into gravitational potential energy: Mgh = (5/6)Mv² Therefore, h = 5v²/(6g) With v = 3 m s⁻¹ and g = 10 m s⁻²: h = 5×9/60 = 0.75 m = 75 cm Final value: 75