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Physics Part-I

System of Particles and Rotational Motion

A solid sphere rolls down on two different inclined planes of

Physics Part-I

Class 11

NCERT

Chapter 1: Physical World

16 questions

Chapter 2: Units and Measurements

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Chapter 3: Motion in Straight Line

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Chapter 4: Motion in a Plane

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Chapter 5: Laws of motion

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Chapter 6: Work, Energy and Power

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Chapter 7: System of Particles and Rotational Motion

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A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?

A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

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Chapter 8: Gravitation

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A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?

Name: Video solution 1: [Solved] A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why? - Physics Part-I
Uploaded: 2022-09-29T10:52:02.000Z
Duration: 6 min
Description: Video solution 1: [Solved] A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why? - Physics Part-I

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Text solutionVerified

(a)

Total energy of sphere at the top=

m g h

At the bottom, the sphere has both translational and rotational energy=

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

Using conservation of energy,

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

......(i)

For solid sphere

I = \frac{2}{5} m r^{2}

......(ii)
Also we have the relation,

v = r ω

.......(iii)

Solving above equations gives

v = \frac{10 g h}{7}

Clearly the speed of sphere at the bottom does not depend on the angle of inclination, both g and h are independent of the angle of inclination.

(b)

Assug rolling without slipping,

I α = F r

(7/5) m r^{2} \times a / r = m g s in (θ) r

a = (5/7) g s in (θ)

Since

θ_{1} < θ_{2}

(c )Acceleration for the less inclined plane is less.
Thus it takes longer time to reach the bottom along the plane with

θ_{1}

inclination.

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Question Text	A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?
Updated On	Sep 29, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	146
Avg. Video Duration	6 min

A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?

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A solid sphere rolls down on two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?

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