Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Class 11

Physics

Motion in a Plane

Uniform circular motion

A stone of mass 250 {~g} is tied to the end of a string of len

Question

Medium

Solving time: 3 mins

A stone of mass $250 g$ is tied to the end of a string of length $1.0 m$ . It is whirled in a horizontal circle with a frequency of $30 rev / min$ .

SELECT MULTIPLE OPTION

The tension in the string changes as the stone moves in the circle.

The tension in the string is constant equal to

\frac{π ^{2}}{4}

newton.

The speed of the stone is

π ms^{- 1}

The maximum speed with which the stone can be whirled is

20 ms^{- 1}

Views: 6,936 students

Book:

IIT JEE Advanced Comprehensive Physics (McGraw Hill)

Found 7 tutors discussing this question

Emma Discussed

A stone of mass

250 g

is tied to the end of a string of length

1.0 m

. It is whirled in a horizontal circle with a frequency of

30 rev / min

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Since the stone is whirled in a horizontal plane, the
weight mg of the stone (which acts vertically down-
wards) is perpendicular to the plane of the circular motion and, therefore, has no component along this plane. Hence the tension in the string is constant.
Given

m = 250 g = 0.25 kg, R = 1.0 m

, frequency

(v)

= 30 rev ./ min = \frac{30}{60} = 0.5 Hz

. Angular frequency

(ω) = 2 π v = 2 π \times 0.5 = π rad s^{- 1}

. The necessary centripetal force is provided by the tension in the string. Therefore,

T = \frac{m v ^{2}}{R} = \frac{m ( ω R ) ^{2}}{R} = m ω^{2} R = 0.25 \times π^{2} \times 1.0 = \frac{π ^{2}}{4} N

Speed of the stone is

v = R ω = 1.0 \times π = π ms^{- 1}

.
The maximum speed is given by

\frac{m v _{m a x}^{2}}{R} = 100

v_{m a x} = \frac{100 \times R}{m} = \frac{100 \times 1.0}{0.25}

= 20 ms^{- 1}

Hence the correct choices are (b), (c) and (d)

Was this solution helpful?

130

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our Physics tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	A stone of mass $250 g$ is tied to the end of a string of length $1.0 m$ . It is whirled in a horizontal circle with a frequency of $30 rev / min$ .
Topic	Motion in a Plane
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	130

A stone of mass $250 g$ is tied to the end of a string of length $1.0 m$ . It is whirled in a horizontal circle with a frequency of $30 rev / min$ .

Text solutionVerified

Practice questions from IIT JEE Advanced Comprehensive Physics (McGraw Hill)

Practice more questions from Motion in a Plane

Practice questions on similar concepts asked by Filo students

A stone of mass 250 g is tied to the end of a string of length 1.0 m. It is whirled in a horizontal circle with a frequency of 30rev/min.

Text solutionVerified

Practice questions from IIT JEE Advanced Comprehensive Physics (McGraw Hill)

Practice more questions from Motion in a Plane

Practice questions on similar concepts asked by Filo students

Related books for questions on Motion in a Plane

A stone of mass $250 g$ is tied to the end of a string of length $1.0 m$ . It is whirled in a horizontal circle with a frequency of $30 rev / min$ .