MCQ
Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is
- ✓$\frac{49}{81}$
- B$\frac{64}{81}$
- C$\frac{8}{9}$
- D$\frac{7}{9}$
✓
Answer
Correct option: A.
$\frac{49}{81}$
(a) : Time period of a simple pendulum,
$
T \propto \sqrt{1} \Rightarrow T^2 \propto l
$
Now, $t=n T \Rightarrow t^2=n^2 T^2 \Rightarrow T^2=\frac{t^2}{n^2}$
$
\therefore \quad \frac{T_1^2}{T_2^2}=\frac{l_1}{l_2} \Rightarrow \frac{l_1}{l_2}=\frac{n_2^2 t^2}{n_1^2 t^2} \Rightarrow \frac{l_1}{l_2}=\frac{49}{81}
$
$
T \propto \sqrt{1} \Rightarrow T^2 \propto l
$
Now, $t=n T \Rightarrow t^2=n^2 T^2 \Rightarrow T^2=\frac{t^2}{n^2}$
$
\therefore \quad \frac{T_1^2}{T_2^2}=\frac{l_1}{l_2} \Rightarrow \frac{l_1}{l_2}=\frac{n_2^2 t^2}{n_1^2 t^2} \Rightarrow \frac{l_1}{l_2}=\frac{49}{81}
$
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