Rolling Motion of Hollow and Solid Cylinders Down Incline

To determine the correctness of the statements, let us analyze the physics of rolling motion down an inclined plane.

Analysis of STATEMENT-1:
Consider a body of mass $M$, radius $R$, and moment of inertia about its central axis $I_{\text{cm}}$ rolling without slipping down an inclined plane of angle $\theta$.

The linear acceleration of the center of mass down the incline is given by:
$a = \frac{g \sin\theta}{1 + \frac{I_{\text{cm}}}{MR^2}}$

1. For the hollow cylinder (thin-walled pipe):
   $I_{\text{cm}} = MR^2 \implies a_{\text{hollow}} = \frac{g \sin\theta}{1 + 1} = \frac{1}{2}g \sin\theta$

2. For the solid cylinder:
   $I_{\text{cm}} = \frac{1}{2}MR^2 \implies a_{\text{solid}} = \frac{g \sin\theta}{1 + \frac{1}{2}} = \frac{2}{3}g \sin\theta$

Since $a_{\text{solid}} > a_{\text{hollow}}$, the solid cylinder accelerates faster.

Given that both cylinders start from rest and travel the same distance $s$ along the incline, the time taken to reach the bottom is:
$t = \sqrt{\frac{2s}{a}}$

Because $a_{\text{solid}} > a_{\text{hollow}}$, we have:
$t_{\text{solid}} < t_{\text{hollow}}$

Hence, the solid cylinder reaches the bottom first, not the hollow cylinder.
Therefore, STATEMENT-1 is False.

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Analysis of STATEMENT-2:
During rolling without slipping, the point of contact is momentarily at rest, so static friction does no work. Consequently, mechanical energy is conserved throughout the motion.

Both cylinders have the same mass $M$ and are released from the same initial height $h$. By the principle of conservation of mechanical energy:
$K_{\text{total}} = \Delta U = Mgh$

where $K_{\text{total}} = K_{\text{trans}} + K_{\text{rot}}$ is the total kinetic energy.

Since the mass $M$ and the vertical drop $h$ are identical for both cylinders, their total kinetic energies at the bottom of the incline must be identical:
$K_{\text{total, hollow}} = K_{\text{total, solid}} = Mgh$

Therefore, STATEMENT-2 is True.

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Conclusion:
STATEMENT-1 is False, and STATEMENT-2 is True.

This corresponds to Option D.