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 increases to $60.5 \; ms^{-1}$. The value of a, in terms of gravitational acceleration g, is closest to :

Solution:

$60 = \sqrt{\frac{Mg}{\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} $

You must select option to get answer and solution

Questions from JEE Main 2019

Physics Most Viewed Questions

6. The spectrum of an oil flame is an example for ...........

KCET 2010 Dual Nature Of Radiation And Matter