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 acceleration a, the wave-speed increases to 60.5 ms^–1. The value of a, in terms of gravitational acceleration g, is closest to :

(1) $g\over5$

(2) $g\over20$

(3) $g\over10$

(4) $g\over30$

Answer 1

Ans: (1) $g\over5$

Sol: $60=\sqrt{Mg\over\mu}$

$60.5=\sqrt{M(g^2+a^2)^{1/2}\over\mu}$

$\implies{60.5\over60}=\sqrt{\sqrt{g^2+a^2\over g^2}}$

$\left(1+{0.5\over60}\right)^4={g^2+a^2\over g^2}=1+{2\over60}$

$\implies g^2+a^2 = g^2+g^2\times{2\over60}$

$a=g\sqrt{2\over60}={g\over\sqrt{30}}={g\over5.47}$

$\approx{g\over5}$