Grade 12IIT JEE Entrance Exam

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

sakshee bansal

11 Years agoGrade 12

1 Answer

Vikas TU

6 Years 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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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

sakshee bansal

1 Answer

Vikas TU

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