Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Two bodies of mass $10\text{ kg}$ and $5\text{ kg}$ moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. Then the ratio between their centripetal acceleration is:

$R/r$

$r/R$

$R^2/r^2$

$r^2/R^2$

Step-by-Step Solution

Formula for Centripetal Acceleration: The centripetal acceleration ( $a_c$ ) of a body moving in a circular path of radius $R$ with angular speed $\omega$ is given by $a_c = \omega^2 R$ .
Angular Speed: The angular speed is related to the time period ( $T$ ) by $\omega = \frac{2\pi}{T}$ .
Application: Since both bodies have the same time period ( $T$ ), they must have the same angular speed ( $\omega$ ). For the first body: $a_1 = \omega^2 R$ For the second body: $a_2 = \omega^2 r$
Ratio: Taking the ratio of their accelerations: $\frac{a_1}{a_2} = \frac{\omega^2 R}{\omega^2 r} = \frac{R}{r}$ . Note that the centripetal acceleration depends only on the radius and angular speed (or period), and is independent of the mass of the body.

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