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System of Particles and Rotational Motion

Conservation of Angular Momentum

A hollow sphere of radius R and mass m is fully filled with wa

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Hard

Solving time: 4 mins

A hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$ . It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$ . If it purely rolls :

Name: Video solution 1: A hollow sphere of radius R and mass m is fully filled with water of mass m. It is rolled down a horizontal plane such that its centre of mass moves with a velocity v. If it purely rolls :
Uploaded: 2023-08-02T11:18:32.000Z
Duration: 10 min
Description: Video solution 1: A hollow sphere of radius R and mass m is fully filled with water of mass m. It is rolled down a horizontal plane such that its centre of mass moves with a velocity v. If it purely rolls :

Kinetic energy of the sphere is

5/6 mv^{2}

Kinetic energy of the sphere is

4/5 mv^{2}

Angular momentum of the sphere about a fixed point on ground is

8/3 mvR

Angular momentum of the sphere about a fixed point on ground is

14/5 mvR

Views: 6,066 students

Updated on: Aug 2, 2023

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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Theodore Discussed

A hollow sphere of radius

R

and mass

m

is fully filled with water of mass

m

. It is rolled down a horizontal plane such that its centre of mass moves with a velocity

v

. If it purely rolls :

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Sol. (C) Total kinetic energy

=

Rotational KE of sphere

+

Translational KE of sphere + Translation KE of water inside it.

K = \frac{1}{2} I ω^{2} + \frac{1}{2} m v^{2} + \frac{1}{2} m v^{2}

\Rightarrow \Rightarrow \Rightarrow K = (\frac{1}{2} \times \frac{2}{3} m R^{2} \times \frac{v ^{2}}{R ^{2}}) + \frac{1}{2} m v^{2} + \frac{1}{2} m v^{2} K = \frac{1}{3} m v^{2} + m v^{2} K = \frac{4}{3} m v^{2}

Angular momentum of sphere about a fixed point on ground,

\Rightarrow \Rightarrow \Rightarrow L = \frac{2}{3} m R^{2} \times \frac{v}{R} + 2 m v R L = \frac{2}{3} m v R + 2 m v R L = \frac{8 m v R}{3}

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Question Text	A hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$ . It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$ . If it purely rolls :
Updated On	Aug 2, 2023
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	241
Avg. Video Duration	10 min

A hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$ . It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$ . If it purely rolls :

Text solutionVerified

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A hollow sphere of radius R and mass m is fully filled with water of mass m. It is rolled down a horizontal plane such that its centre of mass moves with a velocity v. If it purely rolls :

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A hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$ . It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$ . If it purely rolls :