A car is moving with speed v on a banked road | vedclass

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(B) Given: Radius $r = 50 \ m$,width $l = 10 \ m$,height $h = 1.5 \ m$,and acceleration due to gravity $g = 10 \ m/s^2$.For a banked road without fric

Vedclass · Accepted Answer

$8.6$

Vedclass · Answer

(B) Given: Radius $r = 50 \ m$,width $l = 10 \ m$,height $h = 1.5 \ m$,and acceleration due to gravity $g = 10 \ m/s^2$.For a banked road without friction,the condition for safe turning is given by $	an 	heta = \frac{v^2}{rg}$.From the geometry of the banked road,$	an 	heta = \frac{h}{l}$ (assuming small angle approximation).Equating the two,we get $\frac{v^2}{rg} = \frac{h}{l}$.Solving for $v$: $v = \sqrt{\frac{hrg}{l}}$.Substituting the values: $v = \sqrt{\frac{1.5 	imes 50 	imes 10}{10}} = \sqrt{75} \approx 8.66 \ m/s$.Rounding to the nearest given option,$v = 8.6 \ m/s$.

$A$ car is moving with speed $v$ on a banked road of radius $50 \ m$,width $10 \ m$,and height $1.5 \ m$. The velocity $v$ of the car is ......... $m/s$.

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