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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 $$60 cm/s$$ on the string when the car is at rest and $$66 cm/s$$ when the car accelerates on a horizontal road. The acceleration of the car is:


A
6.7m/s2
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B
3.6m/s2
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C
8.5m/s2
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D
1.5m/s2
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Solution

The correct option is C $$6.7 m/s^{2}$$
At rest, $$V_1 = 60cm/s$$, While moving $$V_2=66cm/s$$
Tension in the string while at rest, $$T_1=mg$$
Tension in the string when accelerated, $$T_2=m\sqrt{a^{2}+g^{2}}$$
$$\because \ v \ \alpha \ \sqrt{T}$$
$$\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}}} \Rightarrow \dfrac{60}{66}=\sqrt{\dfrac{mg}{m\sqrt{a^{2}+g^{2}}}}$$
$$\Rightarrow \dfrac{121}{100}=\dfrac{\sqrt{a^{2}+g^{2}}}{g}$$
$$\Rightarrow a^{2}=44.572$$
$$\Rightarrow a=6.676\ ms^{-2}\approx 6.7\ ms^{-2}$$

65474_8215_ans.png

Physics

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