TS EAMCET 5-Aug-2021 Shift 1 Question Paper

Given,
Three bodies be ring, solid cylinder and solid sphere, initial speed (u) be zero.
E‌total ‌=(KE)rot+(KE)‌trans ‌=mgh
h be the height of inclined plane.
∴‌‌‌

1

2

Iω2+‌

1

2

mv2=mgh
⇒‌‌‌

1

2

I‌

v2

R2

+‌

1

2

mv2=mgh
⇒‌‌v2=√‌

2mgh

I R2 +m

where, v= velocity of body at bottom (v=Rω)
I‌‌=‌ moment of inertia, ‌
ω‌‌=‌ angular frequency, ‌
m‌‌=‌ mass of body ‌
‌ and ‌‌‌R‌‌=‌ radius of body. ‌
∵‌‌I‌ring ‌‌‌=MR2
I‌solid cylinder ‌‌‌=‌

MR2

2

=0.5MR2
I‌solid sphere ‌‌‌=‌

2

5

MR2=0.4MR2
∴ From equation v∝‌

1

√I

and I‌ring ‌>I‌solid cylinder ‌>I‌solid sphere ‌
∴v‌ring ‌ is least.