Question

STATEMENT-1
Two cylinders, one hollow (metal) and the 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 cylinder will reach the bottom of the 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 True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
• B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
• C. STATEMENT -1 is True, STATEMENT-2 is False
• D. STATEMENT -1 is False, STATEMENT-2 is True

Answer 1

The correct option is D STATEMENT -1 is False, STATEMENT-2 is True

Time of descent for hollow cylinder is:
$t_{hollow}=\sqrt{\frac{4l}{g\sin \theta }}$
Time of descent for solid cylinder is:
$t_{solid}=\sqrt{\frac{3l}{g\sin \theta }}$
Thus, the solid cylinder will take more time to reach the bottom. Statement-1 is false.
Since they are released from same height and have same mass, their total KE at the bottom will be same.
Hence, option D.