(A) Mass of the stone,$m = 0.25 \; kg$.Radius of the circle,$r = 1.5 \; m$.Frequency of revolution,$n = \frac{40}{60} = \frac{2}{3} \; rps$.Angular ve

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(A) Mass of the stone,$m = 0.25 \; kg$.Radius of the circle,$r = 1.5 \; m$.Frequency of revolution,$n = \frac{40}{60} = \frac{2}{3} \; rps$.Angular velocity,$\omega = 2 \pi n = 2 \times 3.1416 \times \frac{2}{3} \approx 4.189 \; rad/s$.The centripetal force is provided by the tension $T$ in the string: $T = m r \omega^2$.$T = 0.25 \times 1.5 \times (4.189)^2 \approx 6.58 \; N$.For the maximum speed,$T_{\max} = 200 \; N$.Using $T_{\max} = \frac{m v_{\max}^2}{r}$,we get $v_{\max} = \sqrt{\frac{T_{\max} \times r}{m}}$.$v_{\max} = \sqrt{\frac{200 \times 1.5}{0.25}} = \sqrt{1200} \approx 34.64 \; m/s$.

Class 11 Physics Laws of Motion Circular motion with Friction

Medium

$A$ stone of mass $0.25 \; kg$ tied to the end of a string is whirled round in a circle of radius $1.5 \; m$ with a speed of $40 \; rev./min$ in a horizontal plane. What is the tension in the string? What is the maximum speed in $m/s$ with which the stone can be whirled around if the string can withstand a maximum tension of $200 \; N$ (in $; m/s$)?

A
$34.64$
B
$42.26$
C
$26.5$
D
$12.26$

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Laws of Motion

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Circular motion with Friction

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$A$ block $(P)$ is rotating in contact with the vertical wall of a rotor as shown in figures $A$,$B$,and $C$. Find the relation between angular velocities $\omega_A, \omega_B$,and $\omega_C$ such that the block does not slide down. ($R_A < R_B < R_C$ are the radii).

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$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

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The radius of a curved road is $R$,and the width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $V$ can pass safely over it. The value of $h$ is ($g =$ acceleration due to gravity).

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$A$ small object placed on a rotating horizontal turntable just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turntable is doubled,the object slips when its distance from the axis of rotation is (in $, cm$)

$A$ block $(P)$ is rotating in contact with the vertical wall of a rotor as shown in figures $A$,$B$,and $C$. Find the relation between angular velocities $\omega_A, \omega_B$,and $\omega_C$ such that the block does not slide down. ($R_A < R_B < R_C$ are the radii).

$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

If the coefficient of friction between the tires and the road is $\mu$,the maximum safe speed is $10\;m/s$. If the coefficient of friction becomes $\mu' = \frac{\mu}{2}$,what will be the new maximum safe speed?

The radius of a curved road is $R$,and the width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $V$ can pass safely over it. The value of $h$ is ($g =$ acceleration due to gravity).

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