JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Rotational Mechanics

The following bodies,
(1) a ring
(2) a disc
(3) a solid cylinder
(4) a solid sphere
of same mass '

m

' and radius '

R

' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ______
[ Mark the body as per their respective numbering given in the question]

Answer: 4

Solution

A body rolling down an incline without slipping has

a = \frac{g sin θ}{1 + \frac{I}{m R ^{2}}}

so over a common length the shortest time belongs to the smallest value of

\frac{I}{m R ^{2}}

. These ratios are

1

for the ring,

\frac{1}{2}

for the disc and for the solid cylinder, and

\frac{2}{5}

for the solid sphere. The solid sphere, numbered

4

, reaches the bottom first.

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Integer answer

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