Practicing Success
Consider an attractive force which is central but is inversely proportional to the first power of distance. If such a particle is in circular orbit, under such a force, which of the following statements are correct? |
the speed is directly proportional to the square root of orbital radius the speed is independent of radius the period is independent of radius the period is directly proportional to radius |
the period is directly proportional to radius |
$F=\frac{k}{r}=\frac{m v^2}{r}$ $\Rightarrow v=\sqrt{\frac{k}{m}}$ = constant, v is independent of radius. T = $\frac{2 \pi r}{v}$ ⇒ T ∝ r T is directly proportional to the radius. |