Question

You are designing a pendulum clock to have a period of $1.0s$. How long should the pendulum be ?

• A. $0.25m$
• B. $0.50m$
• C. $0.25cm$
• D. $0.25mm$

Answer 1

The correct option is A $0.25m$

$T=2\pi \sqrt{\frac{L}{g}}\Rightarrow T^2=4{\pi }^2\times \frac{L}{g}$ .. (1)

Putting $T=1$ in eqn. (1),

We get $1=4{\pi }^2\times \frac{L}{g}$ $\Rightarrow L=\frac{g}{4{\pi }^2}=\frac{9.8}{4\times 3.14\times 3.14}m\Rightarrow L=\frac{9.8}{39.44}m=0.2484m=0.25m$ (approx.)