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a thin hollow sphere of mass m is completely filled with an ideal solution of liquid with mass m .when the sphere rolls without slipping with a velocity v kinectic energy of system is equal to

a thin hollow sphere of mass m is completely filled  with an ideal solution of liquid with mass m .when the sphere rolls without slipping with a velocity v  kinectic energy of system is equal to

Grade:12

1 Answers

Vikas TU
14149 Points
one year ago
A thin hollow sphere of mass m is completely filled with non - viscous liquid of mass m.
there are two components of kinetic energy of the system, rotational and translational.
rotational kinetic energy is only contributed by hollow sphere as liquid is non-viscous , liquid is presumably not rotating.
so, rotational kinetic energy of hollow sphere = 1/2 Iw²
we know, w is angular frequency i.e., w = v/r
and moment of inertia of hollow sphere about an axis passing through diameter of it , I = 2/3 mr²
so, rotational kinetic energy = 1/2 × 2/3 mv² = 1/3 mv² .....(1)
translational kinetic energy = kinetic energy of hollow sphere + kinetic energy of liquid
= 1/2 mv² + 1/2 mv²
= mv²
now, total kinetic energy = mv² + 1/3mv²
= 4/3 mv²
hence, answer is 4/3 mv²

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