Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Two particles $A$ and $B$ are moving in a uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speeds $v_A$ and $v_B$ respectively. Their time periods of rotation are the same. The ratio of the angular speed of $A$ to that of $B$ will be:

1 : 1

$r_A : r_B$

$v_A : v_B$

$r_B : r_A$

Step-by-Step Solution

Definition of Angular Speed: The angular speed $\omega$ of a particle performing uniform circular motion is related to its time period $T$ (time for one complete revolution) by the formula $\omega = \frac{2\pi}{T}$ .
Analyze the Condition: The problem states that the time periods of rotation for both particles are the same, i.e., $T_A = T_B$ .
Calculate Ratio: $\omega_A = \frac{2\pi}{T_A}$ $\omega_B = \frac{2\pi}{T_B}$ Since $T_A = T_B$ , it implies that $\omega_A = \omega_B$ .
Conclusion: The ratio of their angular speeds is $\omega_A : \omega_B = 1 : 1$ . The radii and linear speeds are not needed to determine this specific ratio given the constant time period condition.

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