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 $60m{s}^{-1}$. When the car has an acceleration a, the wave-speed increases to $60.5m{s}^{-1}$. The value of a, in terms of gravitational acceleration $g$, is closest to :

• A. $\frac{g}{5}$
• B. $\frac{g}{20}$
• C. $\frac{g}{10}$
• D. $\frac{g}{30}$

Answer 1

The correct option is A $\frac{g}{5}$

$60=\sqrt{\frac{Mg}{\mu }}$
$60.5=\sqrt{\frac{M(g^2+a^2{)}^{1/2}}{\mu }}\Rightarrow \frac{60.5}{60}=\sqrt{\sqrt{\frac{g^2+a62}{g^2}}}$
${(1+\frac{05}{60})}^4=\frac{g^2+a^2}{g^2}=1+\frac{2}{60}$
$\Rightarrow g^2+a^2=g^2+g^2\times \frac{2}{60}$
$a=g\sqrt{\frac{2}{60}}=\frac{g}{\sqrt{30}}=\frac{g}{5.47}$
$\simeq \frac{g}{5}$