Question

JEE ADVANCED PHYSICS QUESTION SEPTEMBER 2020

Answer 1

A football of radius R is kept on ahold 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 figure below. The maximum value θ so that the football does not start rolling down the plank satisfies ....

solution : see free body diagram of given situations.

as football doesn't start rolling, it means net torque must be zero.

i.e., net torque = 0

⇒component of torque along plane = component of torque perpendicular to plane

⇒weight along plane × √(R² - r²) = weight along perpendicular to plane × r

⇒mgsinθ√(R² - r²) = mgcosθ r

⇒tanθ = r/√(R² - r²)

so sinθ = r/R

Therefore option (A) is correct choice.