JEE Advanced2018PhysicsRotational MotionActual
A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60 ° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is 2 - 3 / 10 s , then the height of the top of the inclined plane (in meters) is __________. Take g = 10 m s - 2 .
Correct answer
0
Step-by-step solution
a c = g sin θ 1 + I c M R 2 a r i n g = g sin θ 2 a r i n g = 2 g sin θ 3 h sin θ = 1 2 g sin θ 2 t 1 2 ⇒ t 1 = 4 h g sin 2 θ = 16 h 3 g ⇒ h sin θ = 1 2 2 g sin θ 3 t 2 2 ⇒ t 2 = 3 h g sin 2 θ = 4 h g ⇒ 16 h 3 g - 4 h g = 2 - 3 10 h 4 3 - 2 = 2 - 3 h = 2 - 3 3 4 - 2 3 = 3 2 ⇒ h = 3 4 = 0.75 m