Question

A solid sphere of mass m and radius r rolls without slipping on a rough  horizontal surface. If ω be its angular speed about its centre of mass, then  calculate its kinetic energy in terms of given quantities.​

Answer 1

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A solid sphere mass M and radius R rolls on a horizontal surface without slipping. The ratio of rotational K.E. ro total K.E. is:-

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Solution

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Correct option is C)

Angular momentum energy

mass of sphere = m

radius = r

M.O.I =

5

2

mr

2

total energy =K

R

+K

T

K

Total

=

2

1

Iw

2

+

2

1

mv

2

↓

As we know

2

1

×

5

2

mr

2

(

r

2

v

2

)+

2

1

mv

2

V=rw

K

total

=

2

1

(

5

7

)mv

2

Fraction of K.E of rotation

=

K

total

K

R

=

2

1

(

5

7

)MV

2

2

1

(

5

2

)MV

2

=

7

2