Question 187: Work, Energy and Power & Circular Motion

Question

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by $20 \%$, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]

Accepted Answer

$$ \begin{array}{ll}  & v_{\max }=\sqrt{r g\left(\frac{	an 	heta+\mu_s}{1-\mu_s 	an 	heta}ight)} \  & v_{\max } \propto \sqrt{r} \ 	herefore & \frac{v_2}{v_1}=\sqrt{\frac{r_2}{r_1}} \ 	herefore & \left(\frac{v_2}{v_1}ight)^2=\frac{r_2}{r_1} \ 	herefore & r_2=\left(\frac{v_2}{v_1}ight)^2 r_1 . \end{array} $$
When safety speed is increased by $20 \%$,
$$ v_2=1.2 v_1 $$
Also given that, $\mathrm{r}_1=20 \mathrm{~m}$
$$ 	herefore \quad r_2=(1.2)^2 	imes 20=1.44 	imes 20=28.8 \mathrm{~m} $$
$	herefore \quad$ Increase in radius $=28.8-20=8.8 \mathrm{~m}$

Answer

28.8 m

Answer

14.4 m

Answer

8.8 m

Answer

4.8 m

Work, Energy and Power & Circular Motion

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by 20 \%, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]

Choose the correct answer: