(C) The angular speed $\omega$ is defined as $\omega = \frac{2 \pi}{T}$,where $T$ is the time period.Since both cars take the same time $T$ to complet

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(C) The angular speed $\omega$ is defined as $\omega = \frac{2 \pi}{T}$,where $T$ is the time period.Since both cars take the same time $T$ to complete one revolution,$T_1 = T_2 = T$.Therefore,the ratio of their angular speeds is $\frac{\omega_1}{\omega_2} = \frac{2 \pi / T_1}{2 \pi / T_2} = \frac{T_2}{T_1} = 1$.The linear speed $v$ is related to angular speed by $v = R \omega$.Since $\omega_1 = \omega_2$,the ratio of their linear speeds is $\frac{v_1}{v_2} = \frac{R_1 \omega_1}{R_2 \omega_2} = \frac{R_1}{R_2}$.Thus,the ratio of angular speeds is $1$ and the ratio of linear speeds is $\frac{R_1}{R_2}$.

Class 11 Physics 2 Motion in a Plane Mix Examples-Motion in Plane

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$A$ car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take the same time to complete the circles,the ratio of their angular speeds and linear speeds will be .........

A
$\sqrt{\frac{R_1}{R_2}}, \frac{R_1}{R_2}$
B
$1, 1$
C
$1, \frac{R_1}{R_2}$
D
$\frac{R_1}{R_2}, 1$

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Mix Examples-Motion in Plane

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MediumTS EAMCET 2004

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The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_0 = 10 \, m$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $v = 20 \, m/s$,on a horizontal surface? $(g = 10 \, m/s^2)$

DifficultJEE MAIN 2013

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The projectile motion of a particle of mass $5\, g$ is shown in the figure. The initial velocity of the particle is $5 \sqrt{2}\, m/s$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 10^{-2}\, kg \cdot m/s$. The value of $x$,to the nearest integer,is ...... .

DifficultJEE MAIN 2021

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$A$ particle is performing uniform circular motion with angular momentum $L$. If the frequency of motion is doubled and the kinetic energy is halved,the new angular momentum will be

Difficult

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$A$ particle is projected from a point at an angle $\theta$ with the horizontal direction. At any time $t$, if $p$ is the linear momentum, $y$ is the vertical displacement, and $x$ is the horizontal displacement, which of the following graphs does not represent the variation of kinetic energy $KE$ of the particle?

DifficultAP EAMCET 2009

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$A$ car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take the same time to complete the circles,the ratio of their angular speeds and linear speeds will be .........

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$A$ particle is performing uniform circular motion with angular momentum $L$. If the frequency of motion is doubled and the kinetic energy is halved,the new angular momentum will be

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