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  4. A particle moves in a circular orbit under the action of a central attractive force inversely proportional to distance r. The speed of the particle is:

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Q. A particle moves in a circular orbit under the action of a central attractive force inversely proportional to distance r. The speed of the particle is:

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Solution:

Given: centripetal force $ \propto \frac{1}{r} $ $ \frac{m{{\upsilon }^{2}}}{r}\propto \,\frac{1}{r} $ or $ \frac{m{{\upsilon }^{2}}}{r}=\frac{k}{r} $ or $ {{\upsilon }^{2}}=\frac{k}{m} $ or $ {{\upsilon }^{2}}=k $ or $ \upsilon =\text{constant} $ So, speed is independent of r.