(A) The maximum speed $v$ of a car on a level curved road is given by the formula $v = \sqrt{\mu Rg}$,where $\mu$ is the coefficient of friction,$R$ i

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(A) The maximum speed $v$ of a car on a level curved road is given by the formula $v = \sqrt{\mu Rg}$,where $\mu$ is the coefficient of friction,$R$ is the radius of the curve,and $g$ is the acceleration due to gravity.Since $\mu$ and $g$ are constant,we have $v \propto \sqrt{R}$.Therefore,the ratio of the speeds is $\frac{v_2}{v_1} = \sqrt{\frac{R_2}{R_1}}$.Given $v_1 = 30 \, m/s$,$R_1 = 75 \, m$,and $R_2 = 48 \, m$.Substituting these values: $\frac{v_2}{30} = \sqrt{\frac{48}{75}}$.Simplifying the fraction inside the square root: $\frac{48}{75} = \frac{16}{25}$.So,$\frac{v_2}{30} = \sqrt{\frac{16}{25}} = \frac{4}{5}$.$v_2 = 30 \times \frac{4}{5} = 6 \times 4 = 24 \, m/s$.

Class 11 Physics Newton's Laws of Motion and Friction Circular motion with Friction

Medium

$A$ curve on a level road has a radius of $75 \, m$. The maximum speed of a car turning this curved road can be $30 \, m/s$ without skidding. If the radius of the curved road is changed to $48 \, m$ and the coefficient of friction between the tyres and the road remains the same,then the maximum allowed speed would be ......... $m/s$.

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$22$
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$26$
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$28$

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Newton's Laws of Motion and Friction

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Circular motion with Friction

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$(b)$ maximum permissible speed to avoid slipping?

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$A$ car is driven on a banked road of radius of curvature $20 \ m$ with maximum safe speed. In order to increase its safe speed by $10 \%$,the increase in the radius of curvature will be (Angle of banking and friction is unchanged in both the cases.) (in $m$)

The distance between the two tires of a car is $1.5 \, m$. The center of mass of the car is at a height of $2 \, m$ from the ground. To take a turn on a road with a radius of $120 \, m$,the speed of the car should be ........ $m/s$.

$A$ train runs along an unbanked circular track of radius $30 \; m$ at a speed of $54 \; km/h$. The mass of the train is $10^{6} \; kg$. What provides the centripetal force required for this purpose - the engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

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