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(B) Given, $v_1 = 14 \ m/s$ and $v_2 = 28 \ m/s$. For a banked road, the angle of banking $	heta$ is related to the velocity $v$ and radius $r$ by th

Vedclass · Accepted Answer

increase the radius by a factor of $4$

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(B) Given, $v_1 = 14 \ m/s$ and $v_2 = 28 \ m/s$. For a banked road, the angle of banking $	heta$ is related to the velocity $v$ and radius $r$ by the formula: $	an 	heta = \frac{v^2}{rg}$. Rearranging for radius, we get $r = \frac{v^2}{g 	an 	heta}$. Since the ramp is similar, the banking angle $	heta$ remains constant. Thus, $r \propto v^2$. Therefore, $\frac{r_2}{r_1} = \left( \frac{v_2}{v_1} ight)^2 = \left( \frac{28}{14} ight)^2 = (2)^2 = 4$. This implies $r_2 = 4r_1$. Hence, the radius should be increased by a factor of $4$.

$A$ circular freeway entrance and exit are commonly banked to control a moving car at $14 \ m/s$. To design a similar ramp for $28 \ m/s$, one should:

Similar Questions

$A$ car of mass $1000 \, kg$ negotiates a banked curve of radius $90 \, m$ on a frictionless road. If the banking angle is $45^\circ$,the speed of the car is ......... $m \, s^{-1}$.

$Assertion$ : There is a stage when frictional force is not needed at all to provide the necessary centripetal force on a banked road.
$Reason$ : On a banked road,due to its inclination the vehicle tends to remain inwards without any chances of skidding.

Write the formula for the maximum permissible speed of a vehicle moving on a smooth banked circular track.

$A$ truck of mass $2000 \,kg$ is moving along a circular path having a radius of curvature $10 \,m$. If the banking angle is $39^{\circ}$, then the maximum permissible speed of the truck is (Acceleration due to gravity $= 10 \,ms^{-2}$, take $\tan 39^{\circ} = 0.81$). (in $\,ms^{-1}$)

What is optimum speed? Write its equation.

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