Satement-1: two cylinder one hollow (metal) and the other side (wood) with the same mass and identical dimensions are simultaneously allowed to roll wihtout 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 cylinder are identical when they reach the bottom of the incline.

Options

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

Explanation

(d) Statement-1: The acceleration of a body rolling down an inclined
plane is given by
`a=(g sin theta)/(1+(I)/(MR^2))`
For hollow cylinder `(I)/(MR^2) = (MR^2)/(MR^2) =1`
For solied cylinder `(I)/(MR^2) = (1)/(2)MR^2/(MR^2) = (1)/(2)`
`rArr` Acceleration of solid cylinder is more than hollow
cylinder and therfor solid cylinder will reach the
bottom of the inclined plane first.
`:. ` Statement -1 is false
Statement-2: In the case of rolling there will be no heat losses.
Therefore total mechanical energy therefore gets converted into
kinetic energy. In both the case since the initial
potental energy. In both the cases since the initial
potential energy is same, the final kinetic energy will
also be same. Therefore statement -2 is correct.