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System of Particles and Rotational Motion

Conservation of Angular Momentum

A particle is projected horizontally with velocity V_{0}={2 g

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Solving time: 4 mins

A particle is projected horizontally with velocity $V_{0} = 2 g a$ along the smooth inside surface of a fixed hollow hemisphere of inner radius ' $a$ ' at the level of the centre ' $O$ '. The subsequent motion of the particle is confined between the horizontal planes one through the centre and the other at a depth $h$ . Find the value of $h$ :

\frac{3}{2} a

\frac{3 - 1}{3} a

\frac{5 - 1}{2} a

\frac{5}{2} a

Views: 5,349 students

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

Text solutionVerified

Sol. (C) By conserving angular momentum about vertical

axis OP

m v_{0} a = m v a^{2} - h^{2}

By conserving mechanical energy

\frac{1}{2} m v^{2} = \frac{1}{2} m v_{0}^{2} + m g h

From equation (1) and (2) we get

h = \frac{a ( 5 - 1 )}{2}

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A particle is projected horizontally with velocity

V_{0} = 2 g a

along the smooth inside surface of a fixed hollow hemisphere of inner radius '

a

' at the level of the centre '

O

'. The subsequent motion of the particle is confined between the horizontal planes one through the centre and the other at a depth

h

. Find the value of

h

14 mins ago

Discuss this question LIVE

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Question Text	A particle is projected horizontally with velocity $V_{0} = 2 g a$ along the smooth inside surface of a fixed hollow hemisphere of inner radius ' $a$ ' at the level of the centre ' $O$ '. The subsequent motion of the particle is confined between the horizontal planes one through the centre and the other at a depth $h$ . Find the value of $h$ :
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	131

Text solutionVerified

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