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Question:

A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m<<M). When the car is at rest, the speed of transverse waves in the string is 60 ms⁻¹. When the car has an acceleration a, the wave-speed increases to 60.5 ms⁻¹. The value of a, in terms of gravitational acceleration g, is closest to:

g30

g5

g20

g10

Solution:

The correct option is A
60 = √(Mg/μ)
60.5 = √(M(g² + a²)¹/²/μ)
=> 60.5/60 = √(g² + a²)/g
=> (1 + 0.5/60)² = (g² + a²)/g²
=> (1 + 1/120)² = 1 + a²/g²
=> 1 + 2/120 = 1 + a²/g² (approx)
=> a²/g² = 1/60
=> a² = g²/60
=> a = g/√60 ≈ g/8 ≈ g/10 ≈ g5