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Q.

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 increase to 60.5 ms^-1.The value of a, in terms of gravitational acceleration g, is close to.

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a

$\frac{g}{5}$

b

$\frac{g}{20}$

c

$\frac{g}{10}$

d

$\frac{g}{30}$

answer is A.

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Detailed Solution

$V = \sqrt{\frac{M g}{μ}} \Rightarrow \frac{Δ V}{V} = \frac{1}{2} \frac{Δ g}{g}$
$\Rightarrow \frac{0.5}{60} = \frac{1}{2} \frac{(\sqrt{a^{2} + g^{2}} - g)}{g}$
$\frac{1}{60} = 1 + \frac{1}{2} \frac{a^{2}}{g^{2}} - 1 \Rightarrow a^{2} = \frac{g^{2}}{30}$

$\Rightarrow a = \frac{g}{\sqrt{30}} = \frac{g}{5}$ .

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