Keeping the banking angle same , to increase the maximum speed with which a vehicle can traveln on the curve road by `10 %` , the radius of curvature of the road has to be changed from 20 m to

Options

A. `12.1 m`
B. `24.2`m
C. 6m
D. 48 m

Answer

B

Explanation

The safety speed on a banked road is given by
` tan theta = (v^(2))/( r g) `
As ` tan theta ` is to kept constant , ` ( v_(1 )^(2))/( r_(1) g)=(v_(2)^(2))/( r_(2) g)`
` therefore (v_(2) ^(2))/( V_(1)^(2))=(r _(2))/(r_(1)) ` But ` (v_(2))/( V_(1)) = (11) /(10 ) , r_(1) = 20 m `
` therefore R_(2) = r_(1) ((v_(2))/(v_(1)))^(2)`
` therefore r_(2) = 20 xx((11)/(10))^(2) = ( 20xx121)/( 100) = ( 121)/( 5) = 24.2 m`