A simple pendulum with a bob of mass $m$ is suspended from the roof of a car moving with a horizontal acceleration $a.$ Then
A. The string makes an angle of ${\tan ^ – }\left( {\frac{a}{g}} \right)$ with the vertical.
B. The string makes an angle of ${\tan ^ – }\left( {1 – \frac{a}{g}} \right)$ with the vertical.
C. The tension is the string is $m\sqrt {{a^2} + {g^2}} $
D. The tension in the string is $m\sqrt {{g^2} – {a^2}} $
Solution
![](https://blogs.thinkmerit.in/wp-content/uploads/2020/07/image.png)
$$T\cos \theta = mg$$ $$T\sin \theta = ma$$ $$\therefore \quad \tan \theta = \frac{a}{g}$$ $$\quad \quad \theta = {\tan ^ – }\left( {\frac{a}{g}} \right)$$ Tension in the string, $$T = m\sqrt {{g^2} + {a^2}} $$
Hence options (A) and (C) are the correct answers.
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