Question

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of $50cm/s$ on the string when the car is at rest and $52cm/s$ when the car accelerates on a horizontal mad. Then acceleration of the car is

(Take $g=10m/s^2$)

• A. $2.7m/s^2$
• B. $3.7m/s^2$
• C. $2.4m/s^2$
• D. $4.1m/s^2$

Answer 1

The correct option is D $4.1m/s^2$

As we know wave speed is given by

$4v=\sqrt{\frac{T}{m}}$ where $m=$ mass per unit length.

Now at rest:

With respect to image $1$

$T=Mg$

$\therefore v=\sqrt{\frac{Mg}{m}}or,50=\sqrt{\frac{Mg}{m}}\therefore \frac{Mg}{m}={50}^2⟶1$

Now when car accelerate:

With respect to image $2$

$T^1=\sqrt{{\left(Ma\right)}^2+{\left(Mg\right)}^2}\therefore v^2=\sqrt{\frac{T^1}{m}}{52}^2=\frac{M\sqrt{a^2+g^2}}{m}⟶2$

Dividing both equation we get

$\frac{{50}^2}{{52}^2}=\frac{g}{\sqrt{a^2+g^2}}or,\frac{g}{a^2+g^2}=0.924or,g=10m/{sec}^2\therefore a^2=16.64a=4.07m/{sec}^2$