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With all other relevant conditions remaining the same, the speed of a vehicle negotiating a curve is proportional to

(Note: W = Weight of the vehicle)
1. W (1/2)
2. W
3. 1 / W
4. 1 / W (1/2)

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Correct Answer - Option 4 : 1 / W (1/2)

Concept-

The presence of horizontal curve imparts centrifugal force which is a reactive force acting outward on a vehicle negotiating it.

Centrifugal force depends on speed and radius of the horizontal curve and is counteracted to a certain extent by transverse friction between the tire and pavement surface.

On a curved road, this force tends to cause the vehicle to overrun or to slide outward from the center of road curvature.

They are the centrifugal force (P) acting outward, weight of the vehicle (W) acting downward, and the reaction of the round on the wheels (RA and RB).

The centrifugal force and the weight is assumed to be from the center of gravity which is at h units above the ground. Let the wheel base be assumed as b units.

The centrifugal force P in kg/m2 is given by

\(P =\dfrac{WV^2}{gR}\)

Where W is the weight of the vehicle in kg, v is the speed of the vehicle in m/sec, g is the acceleration due to gravity in m/sec2 and R is the radius of the curve in m.

The centrifugal ratio or the impact factor P/W is given by

\(\dfrac{P}{W}=\dfrac{V^2}{gR}\)

So,

\(V=\sqrt{{\dfrac{PgR}{W}}}\)

So from the above equation it can be concluded that velocity is proportional to 1/ W½

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