JEE ADVANCED PHYSICS QUESTION SEPTEMBER 2020
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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.
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