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Problems in General Physics

PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS

Q. 263. A uniform ball of radius r rolls without slipping down

Problems in General Physics

Class 11

IE Irodov

Chapter 1: PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS

277 questions

Q. 262. A uniform solid cylinder of mass

m

and radius

R

is set in rotation about its axis with an angular velocity

ω_{0}

, then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and the plane is equal to

k

. Find: (a) how long the cylinder will move with sliding; (b) the total work performed by the sliding friction force acting on the cylinder

Q. 263. A uniform ball of radius

r

rolls without slipping down from the top of a sphere of radius

R

. Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.

Q. 264. A uniform solid cylinder of radius

R = 15 cm

rolls over a horizontal plane passing into an inclined plane forming an angle

α = 3 0^{\circ}

with the horizontal (Fig. 1.67). Find the maximum value of the velocity

v_{0}

which still permits the cylinder to roll onto the inclined plane section without a jump. The sliding is assumed to be absent.

View all question

Chapter 2: PART TWO. THERMODYNAMICS AND MOLECULAR PHYSICS

9 questions

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46 questions

Chapter 4: PART FOUR. OSCILLATIONS AND WAVES

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215 questions

Chapter 6: PART SIX. ATOMIC AND NUCLEAR PHYSICS

271 questions

Question

Hard

Solving time: 5 mins

Q. 263. A uniform ball of radius $r$ rolls without slipping down from the top of a sphere of radius $R$ . Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.

Name: Video solution 1: [Solved] Q. 263. A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R. Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible. - Problems in General Physics
Uploaded: 2022-11-17T15:31:40.000Z
Duration: 12 min
Description: Video solution 1: [Solved] Q. 263. A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R. Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible. - Problems in General Physics

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Updated on: Nov 17, 2022

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Problems in General Physics (IE Irodov)

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Q. 263. A uniform ball of radius

r

rolls without slipping down from the top of a sphere of radius

R

. Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Let us write the equation of motion for the centre of the sphere at the moment of breaking-off:

m v^{2} / (R + r) = m g cos θ

where

v

is the velocity of the centre of the sphere at that moment, and

θ

is the corresponding angle (Fig.). The velocity can be found from the energy conservation law :

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

where

I

is the moment of inertia of the sphere relative to the axis passing through the sphere’s centre. i.e.

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

. In addition,

v = ω r; h = (R + r) (1 - cos θ)

From these four equations, we obtain

ω = 10 g (R + r) 17 r^{2}

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Question Text	Q. 263. A uniform ball of radius $r$ rolls without slipping down from the top of a sphere of radius $R$ . Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.
Updated On	Nov 17, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	154
Avg. Video Duration	12 min

Q. 263. A uniform ball of radius $r$ rolls without slipping down from the top of a sphere of radius $R$ . Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.

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Q. 263. A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R. Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.

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Q. 263. A uniform ball of radius $r$ rolls without slipping down from the top of a sphere of radius $R$ . Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.