JEE Mains · Physics · STD 11 - 7. gravitation
A test particle is moving in a circular orbit in the gravitational field produced by a mass density \(\rho \left( r \right) = \frac{K}{{{r^2}}}\). Identify the correct relation between the radius \(R\) of the particle’s orbit and its period \(T\)
- A \(T/R^2\) is a constant
- B \(TR\) is constant
- C \(T^2/R^3\) is a constant
- D \(T/R\) is a constant
Answer & Solution
Correct Answer
(D) \(T/R\) is a constant
Step-by-step Solution
Detailed explanation
For circular motion of particle: \(\frac{{m{V^2}}}{r} = mE\) \( = m\left( {\frac{{GM}}{{{r^2}}}} \right)\) where \(M = \int\limits_0^r {\left( {4\pi {x^2}dx} \right)} \left( {\frac{k}{{{x^2}}}} \right)\) \( = 4\pi kr\)…
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