SATHEE: System of Particles and Rotational Motion

System of Particles and Rotational Motion - Result Question 11

11. Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. Their time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be :

[2019]

(a) $r_{A} : r_{B}$

(b) $v_{A} : v_{B}$

(c) $r_{B} : r_{A}$

(d) $1 : 1$

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Answer:

Correct Answer: 11. (d)

Solution:

(d) Let $T_{A}$ and $T_{B}$ are the time periods of particle $A$ and $B$ respectively. According to question,

$T_{A} = T_{B} = T$

If $ω_{A}$ and $ω_{B}$ are their angular speeds, then

$ω_{A} = \frac{2 π}{T_{A}}$ and $ω_{B} = \frac{2 π}{T_{B}}$

$∴ \frac{ω_{A}}{ω_{B}} = \frac{T_{B}}{T A} = \frac{T}{T} = 1 : 1$

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System of Particles and Rotational Motion - Result Question 11

11. Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

Answer:

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11. Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. Their time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be :