Question

Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $ 7:8, $ then the ratio of lengths of the two pendulums will be

• A. $ 7:8 $
• B. $ 8:7 $
• C. $ 49:64 $
• D. $ 64:49 $

Answer 1

Answer: (D)

Suppose at $t =0$, pendulums beings to given $r_o$ swing simultaneously.
Hence they will again swing simultaneously
if $n _{1} T _{1}= n _{2} T _{2}$
$\Rightarrow \frac{ n _{1}}{ n _{2}}=\frac{ T _{2}}{ T _{1}}=\sqrt{\frac{ l _{2}}{ l _{1}}}$
$\Rightarrow \frac{ l _{1}}{ l _{2}}=\left(\frac{ n _{2}}{ n _{1}}\right)^{2}$
$=\left(\frac{8}{7}\right)^{2}=\frac{64}{49}$