QJEEM18Ph4014: JEE Main 2018 Physics - Class 11 JEEM18Ph4014 Solution: A particle is moving with a uniform speed in a circular orbit…

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QJEEM18Ph4014: JEE Main 2018 Physics - Class 11 JEEM18Ph4014 Solution: A particle is moving with a uniform speed in a circular orbit…

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 :

Multiple Choice Options

A T ∝ Rn/2
B T ∝ R3/2 for any n
C T ∝ Rn/2 +1
D T ∝ R(n+1)/2

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Accepted Answer

We know, Central force in circular motion, F =

m ω^{2} R

According to the question,

F \propto \frac{1}{R^{n}}

∴

m ω^{2} R

\propto \frac{1}{R^{n}}

\Rightarrow m ω^{2} R = \frac{k}{R^{n}}

\Rightarrow ω^{2} = \frac{k}{m R^{n + 1}}

∴

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

.......(1)

And we know,

T = \frac{2 π}{ω}

∴

T \propto \frac{1}{ω}

...... (2)

From (1) and (2) we can conclude that,

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

QJEEM18Ph4014: JEE Main 2018 Physics - Class 11 JEEM18Ph4014 Solution: A particle is moving with a uniform speed in a circular orbit…

Multiple Choice Options

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