What is the kinetic energy of a 5.0 kg solid ball whose diameter is 15 m if it rolls across a level surface with a speed of 2m s⁻¹? (14J) 


Given:

Mass of Solid Ball (sphere) = 5.0 kg
Diameter of Solid Ball (sphere) = d = 15 m, So
Radius of Solid Ball (sphere) = r = `\frac {d}{2}` = `\frac {15 m}{2}` = 7.5 m
Linear speed = v = 2m s⁻¹

To Find:

Kinetic Energy of Solid Ball (sphere) = K.E. = ?

Solution:

For rolling motion, the  K.E. total is the sum of the Linear K.E. and Rotational K.E.

K.E. total = K.E. linear + K.E. rotational

K.E. total = `\frac {1}{2}`mv² + IѠ²

As I = `\frac {1}{2}`mr² and Ѡ = `\frac {v}{r}`, So

K.E. total = `\frac {1}{2}`mv² + `\frac {1}{2}`mr² ｘ(`\frac {v}{r}`)²

by putting values

K.E. total = `\frac {1}{2}`5.0 kg ｘ( 2m s⁻¹ )² + `\frac {1}{2}`5.0 kg ｘ(7.5 m)² ｘ(`\frac {2 m s⁻¹}{7.5 m}`)²

K.E. total = 10 kg m² s⁻² + 140.625 kg m² ｘ0.071 s⁻²

K.E. total = 10 kg m² s⁻² + 10 kg m² s⁻²

K.E. total = 20 kg m² s⁻²

or

K.E. total = 20 J -----------Ans.


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