Answer :
Answer:
[tex]\dfrac{KE_R}{KE_L}=\dfrac{2}{5}[/tex]
Explanation:
given,
mass of solid sphere = M
radius = R
linear speed = v
now,
Linear Kinetic energy
[tex] KE_L = \dfrac{1}{2}mv^2[/tex]...............(1)
Rotational kinetic energy
[tex] KE_R= \dfrac{1}{2}I\omega^2[/tex]
moment of inertia of the solid sphere
[tex]I = \dfrac{2}{5}MR^2[/tex]
and v = R ω
[tex] KE_R= \dfrac{1}{2}(\dfrac{2}{5}MR^2)(\dfrac{v}{R})^2[/tex]
[tex]KE_R =\dfrac{1}{5}MV^2[/tex]............(2)
ration of rotational and Kinetic energy
[tex]\dfrac{KE_R}{KE_L}=\dfrac{\dfrac{1}{5}MV^2}{\dfrac{1}{2}MV^2}[/tex]
[tex]\dfrac{KE_R}{KE_L}=\dfrac{2}{5}[/tex]
hence, ratio of rotational to linear kinetic energy is equal to 2/5.