Question

A hollow sphere is kept with a spin w gently on a rough horizontal floor .Find the fraction of total energy lost during sliding​

Answer 1

Explanation:

Let sphere of mass is M and radius is R.

Moment of inertia(MOI), I=

3

2

MR

2

Hollow sphere is rolling without slipping. ⇒v=Rω, Wherev is speed of centre of mass and ω is angular speed.

⇒ Translational KInetic Energy=

2

1

Mv

2

⇒ Rotational KInetic Energy=

2

1

Iω

2

=

2

1

×(

3

2

MR

2

)×(

R

v

)

2

=

3

1

Mv

2

⇒ Total Kinetic Energy=

2

1

Mv

2

+

3

1

Mv

2

=

6

5

Mv

2

⇒ % of Translational Energy=

6

5

Mv

2

2

1

Mv

2

×100=60%

Answer 2

Answer:

Bernoulli's eqn =

Pressure at top = P°(atm.p)

pressure at bottom =( p°+ rho.g.h)

How did you cancel both ?