JEE Advanced2020PhysicsRotational MotionActual
A football of radius R is kept on a hole of radius r ( r R ) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle θ from the horizontal as shown in the figure below. The maximum value of θ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)
Options
- Asin θ = r R
- Btan θ = r R
- Csin θ = r 2 R
- Dcos θ = r 2 R
Correct answer
A. sin θ = r R
Step-by-step solution
m g sin θ R 2 − r 2 = m g cos θ r ⇒ tan θ = r R 2 − r 2 ⇒ sin θ = r R