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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A heavy ball of mass $M$ is suspended from the ceiling of 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
  • A
    $\frac{g}{{30}}$
  • B
    $\frac{g}{{10}}$
  • ✓
    $\frac{g}{{5}}$
  • D
    $\frac{g}{{20}}$
✓

Answer

Correct option: C.
$\frac{g}{{5}}$
c
$60=\sqrt{\frac{M g}{\mu}}$

$60.5=\sqrt{\frac{M\left(g^{2}+a^{2}\right)^{1 / 2}}{\mu}} \Rightarrow \frac{60.5}{60}=\sqrt{\sqrt{\frac{g^{2}+a^{2}}{g^{2}}}}$

$\left(1+\frac{0.5}{60}\right)^{4}=\frac{g^{2}+a^{2}}{g^{2}}=1+\frac{2}{60}$

$\Rightarrow g^{2}+a^{2}=g^{2}+g^{2} \times \frac{2}{60}$

$a=g \sqrt{\frac{2}{60}}=\frac{g}{\sqrt{30}}=\frac{g}{5.47}$

$\simeq \frac{g}{5}$

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