Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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

Proportional to $r^2$

Independent of $r$

Proportional to $r$

Proportional to $1/r$

Step-by-Step Solution

Identify Forces: For a particle moving in a circular orbit, the centripetal force required is provided by the given central attractive force.
Centripetal Force Formula: The centripetal force acting on a particle of mass $m$ moving with speed $v$ in a circle of radius $r$ is $F_c = \frac{mv^2}{r}$ [Source 61].
Given Force Law: The problem states the attractive force $F$ is inversely proportional to distance $r$ . So, $F \propto \frac{1}{r}$ or $F = \frac{k}{r}$ where $k$ is a constant.
Equate Forces: $\frac{mv^2}{r} = \frac{k}{r}$
Solve for Speed ( $v$ ): Multiplying both sides by $r$ eliminates it from the equation. $mv^2 = k$ $v = \sqrt{\frac{k}{m}}$
Conclusion: Since $k$ and $m$ are constants, the speed $v$ is constant and independent of $r$ .

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