Question

if effective length of a simple pendulum is equal to radius of earth R time period willbe

Answer 1

time period
T=2π√l/√g
=2×3.14√6400/√9.8
=84.6

Answer 2

The time period is $\bold{5.09 \times 10^{3}}$ per sec  when simple pendulum effective length is equal to earth radius R.

Solution:

According to the question, the radius of Earth, if taken to be the effective length assuming to be of simple pendulum, the time period is calculated as follows,

Given: Arm length l = R

As we know that the Radius of earth is 6400 km = $6.38 \times 10^{6} m$  

The formula of time period T is –

$\begin{array}{l}{T=2 \pi \sqrt{\frac{l}{g}}} \\ {T=2 \pi \sqrt{\left(\frac{R}{g}\right)}} \\ {T=2 \pi \sqrt{\frac{6400 \mathrm{km}}{9.8 \frac{\mathrm{m}}{\mathrm{s}}}}}\end{array}$

$\begin{array}{l}{T=2 \pi \sqrt{\frac{6.38 \times 10^{6}}{9.8}}} \\ {T=2 \times 3.14 \sqrt{0.65 \times 10^{6}}} \\ {T=2 \times 3.14 \times 0.81 \times 1000}\end{array}$

T=$\bold{5.09 \times 10^{3} per sec}$