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 50 cm/s on the string when the car is at rest and 52 m/s when the car accelerates on a horizontal road. Then acceleration of the car is (Take g = 10 $m/s^2$)

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

Answer 1

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

Let the acceleration of the car be = a

$v=\sqrt{\frac{T}{\mu }}\Rightarrow 50=\sqrt{\frac{mg}{\mu }}$

Let $\frac{T}{\mu }=x\therefore 50=\sqrt{xg}\Rightarrow x=\frac{2500}{10}=250T^1=\sqrt{{\left(ma\right)}^2+{\left(mg\right)}^2}=m\sqrt{g^2+a^2}{v}^1=\sqrt{\frac{T^1}{\mu }}=\sqrt{\frac{m\sqrt{g^2+a^2}}{\mu }}{v}^1=\sqrt{250\sqrt{g^2+a^2}}{\left(52\right)}^2=250\sqrt{g^2+a^2}\frac{2704}{250}=\sqrt{g^2+a^2}{\left(10.8\right)}^2=100+a^{2}116.64-100=a^2\Rightarrow a^2=16.64[a=4.07m/s^2]$

Thus the acceleration of car is $4.07m/s^2$

Hence option (D) is correct