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:

Question

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: (A) proportional to r2  (B) independent of r (C) proportional to r (D) proportional to 1/r

Tardigrade Admin · Accepted Answer

Given: centripetal force propto (1/r) (m upsilon 2/r) propto (1/r) or (m upsilon 2/r)=(k/r) or upsilon 2=(k/m) or upsilon 2=k or upsilon = textconstant So, speed is independent of r.

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:

proportional to $r^{2}$

independent of r

proportional to r

proportional to 1/r

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