(D) The centripetal force $F$ acting on a body of mass $m$ moving in a circle of radius $r$ with angular velocity $\omega$ is given by $F = m r \omega

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(D) The centripetal force $F$ acting on a body of mass $m$ moving in a circle of radius $r$ with angular velocity $\omega$ is given by $F = m r \omega^2$.Since both cars complete their circles in the same time $t$,their angular velocities are equal: $\omega = \frac{2\pi}{t}$.Therefore,the ratio of the centripetal forces $F_{1}$ and $F_{2}$ is:$\frac{F_{1}}{F_{2}} = \frac{m_{1} r_{1} \omega^2}{m_{2} r_{2} \omega^2} = \frac{m_{1} r_{1}}{m_{2} r_{2}}$.Thus,the ratio is $m_{1} r_{1} : m_{2} r_{2}$.

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

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Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal force is

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$m_{1}: m_{2}$
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$r_{1}: r_{2}$
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$1: 1$
D
$m_{1} r_{1}: m_{2} r_{2}$

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Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal force is

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$A$ body is projected at $t=0$ with a velocity of $10 \ m/s$ at an angle of $60^{\circ}$ with the horizontal. The radius of curvature of its trajectory at $t=1 \ s$ is $R$. Neglecting air resistance and taking acceleration due to gravity $g=10 \ m/s^2$, the value of $R$ is: (in $m$)

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An insect trapped in a circular groove of radius $12 \; cm$ moves along the groove steadily and completes $7$ revolutions in $100 \; s$.
$(a)$ What is the angular speed,and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector? What is its magnitude?