AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

The velocity of the solid sphere is v=4

m

s

The figure below represents the solid sphere moves along the inclined plane.
The kinetic energy at the bottom, is equal to the sum of kinetic energy due or translation and rotation,
KE=KEt+KE
=

1

2

mv2+

1

2

Iω2
=

1

2

mv2+

1

2

(

2

5

mr2 )(

v2

r2

)2
=

1

2

(

7

5

mv2)
From the conservation of energy, at height h
KE=mgh

1

2

(

7

2

mv2)=mgh

1

2

(

7

2

(4)2)=(10)h
h=1.12m
The maximum distance travelled is,
l=

h

sin‌30°

I=

1.12

sin‌30°

l=22.4m