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A boy timed 30 oscillations of a certain pendulum thrice and obtained \(1 min .10 s , 1 ...
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A boy timed 30 oscillations of a certain pendulum thrice and obtained \(1 min .10 s , 1 min\). \(12 s\) and \(1 min 7 s\) respectively. the mean period of oscillation of the pendulum is
A.
0.14 s
B.
0.43 s
C.
2.32 s
D.
6.97 s
Show Answer
Show Explanation
Correct Answer: C
Explanation
\(1 \min 10 sec =70 sec\)
\(1 \min 12 sec =72 sec\)
\(1 \min 7 sec =67 sec\)
$$
T_{1}=\frac{t_{1}}{n}, T_{2}=\frac{t_{2}}{n}, T_{3}=\frac{t_{3}}{n}
$$verage \(=\frac{T_{1}+T_{2}+T_{3}}{3}\)
$$
\begin{aligned}
&=\frac{\frac{t_{1}}{n}+\frac{t_{2}}{n}+\frac{t_{3}}{n}}{3} \\
&=\frac{1}{3 n}\left(t_{1}+t_{2}+t_{3}\right) \\
&=\frac{70+72+67}{90}=2.32 sec .
\end{aligned}
$$
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