Question:
If a body moving in a circular path maintains constant speed of \(10\ \mathrm{m\,s^{-1}}\), then which of the following correctly describes the relation between acceleration and radius?
If a body moving in a circular path maintains constant speed of \(10\ \mathrm{m\,s^{-1}}\), then which of the following correctly describes the relation between acceleration and radius?
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For constant speed v, centripetal acceleration is v^2/r, so a is inversely proportional to r.
Updated On: Nov 11, 2026
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The Correct Option is D
Solution and Explanation
Centripetal acceleration \(a=\frac{v^2}{r}=\frac{100}{r}\) with v fixed at 10 m/s.
So \(a\propto\frac1r\), a rectangular hyperbola: a is very large for small r and falls towards zero for large r.
Graph (4) shows this decreasing hyperbolic curve (graph (1) is constant, (2) and (3) are increasing).
Answer: (4) (decreasing hyperbola graph)
So \(a\propto\frac1r\), a rectangular hyperbola: a is very large for small r and falls towards zero for large r.
Graph (4) shows this decreasing hyperbolic curve (graph (1) is constant, (2) and (3) are increasing).
Answer: (4) (decreasing hyperbola graph)
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