Question

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of 60 cm/s on the string when the car is at rest and 62 cm/s when the car accelerates on a horizontal road. Then acceleration of the car is : (take g = 10 m/s2)

Answer 1

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Answer 2

Acceleration of the car = 3.76 m/s2

Explanation:

Let mass of the heavy ball be M and mass per unit length be m.

Wave speed, v1 = root of (T/m) = root of (Mg/m) = 60, as T = Mg

Mg/m = 60^2 ----------------- (1)

For the free body, v2 = root of (T1/m)

v2 = [(Ma)^2 + (Mg)^2]^1/4 / m^1/2 as T = root of [(Ma)^2 + (Mg)^2]

62 = [(Ma)^2 + (Mg)^2]^1/4 / m^1/2

62^2 = root of [(Ma)^2 + (Mg)^2] / m -------------(2)

Adding both the equations, we get:

(Mg/m) * m / root of [(Ma)^2 + (Mg)^2] = 60 * 60 / 62 * 62

g / root of (a^2 + g^2) = 0. 936

Squaring on both sides, we get g^2 / (a^2 +g^2) = 0.876

Taking g = 10 m/s2,

(a^2 + 100) 0.876 = 100

a^2 * 0.876 = 100 - 87.6

a^2 = 12.4 / 0.876 = 14.15

There a = root of 14.15 = 3.76 m/s2