A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of $60 c m / s$ on the string when the car is at rest and $66 c m / s$ when the car accelerates on a horizontal road. The acceleration of the car is:

6.7 m / s^{2}

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3.6 m / s^{2}

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8.5 m / s^{2}

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1.5 m / s^{2}

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Solution

The correct option is C $6.7 m / s^{2}$
At rest, $V_{1} = 60 c m / s$ , While moving $V_{2} = 66 c m / s$
Tension in the string while at rest, $T_{1} = m g$
Tension in the string when accelerated, $T_{2} = m \sqrt{a^{2} + g^{2}}$
$∵ v α \sqrt{T}$
$∴ \frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow \frac{60}{66} = \sqrt{\frac{m g}{m \sqrt{a^{2} + g^{2}}}}$
$\Rightarrow \frac{121}{100} = \frac{\sqrt{a^{2} + g^{2}}}{g}$
$\Rightarrow a^{2} = 44.572$
$\Rightarrow a = 6.676 m s^{- 2} \approx 6.7 m s^{- 2}$

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A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of 60cm/s on the string when the car is at rest and 66cm/s when the car accelerates on a horizontal road. The acceleration of the car is:

The correct option is C 6.7m/s2At rest, V1=60cm/s, While moving V2=66cm/sTension in the string while at rest, T1=mgTension in the string when accelerated, T2=m√a2+g2∵ v α √T∴v1v2=√T1T2⇒6066=√mgm√a2+g2⇒121100=√a2+g2g⇒a2=44.572⇒a=6.676 ms−2≈6.7 ms−2

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of $60 c m / s$ on the string when the car is at rest and $66 c m / s$ when the car accelerates on a horizontal road. The acceleration of the car is: