Question

Statement -1 —Two cylinder one hollow and other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow will reach the bottom of inclined plane first. 

Statement -2 — By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline. 

(A) Statement - 1 is correct (true), Statement - 2 is true and Statement- 2 is correct explanation for Statement - 1 

(B) Statement -1 is true, statement -2 is true but statement-2 is not the correct explanation four statement -1. 

(C) Statement - 1 is true, statement-2 is false 

(D) Statement-2 is false, statement -2 is true

Answer 1

Correct option: (D) Statement-2 is false, statement -2 is true

Explanation:

acceleration = a ∙ [(gsinθ) / {1 + (I_CM / mR²)}]

For hollow cylinder I_CM = mR² = Ih

Solid cylinder I_CM = [(mR²) / ∝] = I_s 

i.e I_h > I_s 

hence a_h < a_s 

hence solid cylinder will reach bottom first.

Also

by
principle of conservation of energy.

KE at bottom = PE = mgh

hence KE is same for each cylinder at bottom (m, h same)