Question

Two pendulums begin to swing simultaneously. The first pendulum makes 9 full oscillations when the other makes 7. Find the ratio of the length of the two pendulums.

• A. $\frac{49}{81}$
• B. $\frac{7}{9}$
• C. $\frac{50}{11}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{49}{81}$

Let time be 'T'

Time period of 1st pendulum be $T_1$

Time period of 2nd pendulum $T_2$

Now $T_1\propto \sqrt{l_1}{T}_2\propto \sqrt{l_2}$

$l_1$ = length of 1st pendulum

$l_2$=length of 2nd pendulum

Again $T=9T_1=7T_2\Rightarrow \left(\frac{T_1}{T_2}\right)=\frac{7}{9}\Rightarrow \sqrt{\frac{l_1}{l_2}}=\frac{7}{9}\Rightarrow \frac{l_1}{l_2}=\frac{49}{81}$

| total time = Time period and no.of full oscillate