Question

A railway line of length 31.4m is to curve through 10°. If the line forms an arc of a circle, then find the radius of curvature of the circle

Answer 1

Let us suppose, if—

L = length of the arc, (given→ 40 m)

ϴ = angle subtended by the arc, (given → 25° )

r = radius of the circle, then

L = ϴ x r —————→ (equation)

then change the angle subtended by arc in radian,

i.e., 25° = 25 x ( π /180) radians,

Now, put all the values in above equation,

40 = (25π /180) x r

=> r = (40 x 180) / (25 π)

putting π = 22/7,

=> r = (288 x 7) / 25

=> r = 91.63 m

Answer 2

Answer:

180 m

Explanation:

we know that: s=rQ

where s=lenghth

r=radius

Q=Angular displacement

B.T.P;

s=r×Q

31.4m=r× 10°

(10°=0.175 rad)

therefore;

r=180m approx