Question

A road is $10m$wide. Its radius of curvature is $50m$. The outer edge is above the lower edge by a distance of $1./5m$. This road is most suited for the velocity

• A. $2.5m/sec$
• B. $4.5m\sec$
• C. $6.5m\sec$
• D. $8.5m\sec$

Answer 1

Answer: (A)

$2.5m/sec$

Let, the angle of inclination $=x$

then,

$tan\left(x\right)=\frac{v^2}{\left(rg\right)}$ ( Can be obtained easily when F.B.D is drawn)

So, in this situation we can take

for very small angle x,

we can take

$sin\left(x\right)=tan\left(x\right)$ ........ (almost equal)

$=>\frac{1.5}{10}=\frac{v^2}{(50\times 9.81)}$

$=>v^2=0.15\times 50\times 9.81$

$=>v=\sqrt{73.575}=8.575m/sec$

______________________