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System of Particles and Rotational Motion

Angular displacement, angular velocity, angular acceleration

A particle is moving with a uniform speed in a circular orbit

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Solving time: 3 mins

A particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the $n$ th power of $R$ . If the period of rotation of the particle is $T$ , then:
(a) $T \propto R^{3/2}$ for any $n$
(b) $T \propto R^{\frac{n}{2} + 1}$
(c) $T \propto R^{(n + 1) /2}$
(d) $T \propto R^{n /2}$

Views: 5,878 students

Updated on: Aug 1, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2018

Text solutionVerified

Exp. (c)

∵

Force

=

Mass

\times

Acceleration

= m ω^{2} R

and given,

F \propto \frac{1}{R ^{n}} \Rightarrow F = \frac{k}{R ^{n}}

So, we have

\frac{k}{R ^{n}} = m (\frac{2 π}{T})^{2} R

\Rightarrow

T^{2} = \frac{4 π ^{2} m}{k} \cdot R^{n + 1}

\Rightarrow T \propto R^{\frac{n + 1}{2}}

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Henry Discussed

A particle is moving with a uniform speed in a circular orbit of radius

R

in a central force inversely proportional to the

n

th power of

R

. If the period of rotation of the particle is

T

, then:
(a)

T \propto R^{3/2}

for any

n

(b)

T \propto R^{\frac{n}{2} + 1}

(c)

T \propto R^{(n + 1) /2}

(d)

T \propto R^{n /2}

10 mins ago

Discuss this question LIVE

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Question Text	A particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the $n$ th power of $R$ . If the period of rotation of the particle is $T$ , then: (a) $T \propto R^{3/2}$ for any $n$ (b) $T \propto R^{\frac{n}{2} + 1}$ (c) $T \propto R^{(n + 1) /2}$ (d) $T \propto R^{n /2}$
Updated On	Aug 1, 2023
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 6
Upvotes	612
Avg. Video Duration	7 min

Text solutionVerified

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A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:(a) T∝R3/2 for any n(b) T∝R2n​+1(c) T∝R(n+1)/2(d) T∝Rn/2

Text solutionVerified

Video solutions (6)

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