Question

The length of a second pendulum is 100 cm whose time period is 1.4 sec.

Answer 1

Step 1: Given data

We know a second pendulum is a pendulum whose time period is 2 sec.

Thus, the time period of seconds pendulum $T_1=2sec$

Length of a seconds pendulum is $L_1=2sec$

Time period of a simple pendulum $T_2=1.4sec$

Length of a simple pendulum $=L_2$

Step 2: Relationship between time period and length

We know that the time period is directly proportional to the square root of the length

$$\begin{gathered} T\propto \sqrt{L} \\ were,T=timeperiodofapendulum \\ L=effectivelength \end{gathered}$$

Hence it can be written as,

$$\begin{gathered} T^2=L \\ whereT=timeperiodofapendulum \\ L=effectivelength \end{gathered}$$

Step 3: Calculate the length of a simple pendulum (L₂)

$$\begin{gathered} \sqrt{\frac{L_1}{L_2}}=\frac{T_1}{T_2} \\ \sqrt{\frac{100cm}{L_2}}=\frac{2sec}{1.4sec} \\ Takingsquareonbothsides, \\ {\left(\sqrt{\frac{100cm}{L_2}}\right)}^2={\left(\frac{2}{1.4}\right)}^2 \\ \frac{100}{L_2}=\frac{4}{1.96} \\ {L}_2=\frac{100\times 1.96}{4} \\ =49cm \end{gathered}$$

Hence, the length of a simple pendulum is 49 cm.