IIT JEE Advanced 2008 Paper 1

For rolling down the incline, we have
a =

gsinθ

1+( k2 r2 )

u = 0; s = l, (say)
Now, l =

1

2

[

gsinθ

1+( k2 r2 )

]t2 =

1

2

[

gsinθ

1+( I mr2 )

]t2
⇒ t2 =

2l[1+( I mr2 )]

gsinθ

where I is the moment of inertia and k is the radius of gyration,
If I is less, the time taken t is also less. For hollow cylinder, we have
I1 = mr2
For solid cylinder, we have
I2 =

mr2

2

< I1
Therefore, the solid cylinder reaches the bottom first; hence, Statement-1 is false.
The total K.E. of both cylinders on reaching the bottom is same by the principle of conservation of energy, which is equal to mgh (for each cylinder), where h is the height of the incline.