Question

The maximum safe speed, for which a banked road is intended, is to be increased by 20 %. If the angle of banking is not changed, then the radius of curvature of the road should be changed from 30 m to ____________.

पर्याय

• 36 m

• 24 m

• 43.2 m

• 60 m

Answer 1

The maximum safe speed, for which a banked road is intended, is to be increased by 20 %. If the angle of banking is not changed, then the radius of curvature of the road should be changed from 30 m to 43.2 m.

Explanation:

Let initial velocity = v1

`"New velocity v"_2 = "v"_1 (1 + 20/100) = (6"v"_1)/5`

`"r"_1 = 30  "m", tan theta_1 = "v"_1^2/("r"_1"g"), tan theta_2 = "v"_2^2/("r"_2"g")`

As there is no change in angle of banking,

`theta_1 = theta_2`

`therefore "tan"  theta_1 = "tan"  theta_2`

`therefore "v"_1^2/("r"_1"g") = "v"_2^2/("r"_2"g")`

`therefore "r"_1/"r"_2 = ("v"_1/"v"_2)^2 = ("v"_1/(6/5"v"_1))^2 = (5/6)^2 = 25/36`

`therefore "r"_2 = 36/25  "r"_1 = 36/25 xx 30 = 216/5 = 43.5  "m"`