Question

A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing. The length of a seconds pendulum in Tokyo, Japan is 0.9927 m and that in Cambridge, England is 0.9942 m. The ratio of the acceleration due to gravity at the two places, gT /gL is

Answer 1

0.9987.
1.0150.
1.0008.
1.0015.
1.0000.
which one is correct !!

Answer 2

The period of the pendulum is given by:
\[\huge{T=2\pi \sqrt{\frac{L}{g}}}\]
Since the period of each pendulum is the same you can set them equal to each other through equations:
\[\huge{T_{T}=T_{C}}\]
\[\huge{2\pi \sqrt{\frac{L_T}{g_T}}=2\pi \sqrt{\frac{L_C}{g_C}}}\]
From here you should be able to rearrange to solve the ratio:
\[\huge{\frac{g_T}{g_C}=?}\]

Answer 3

is the period of a pendulum a given formula?

Answer 4

yes...see first equation above.
T = Period
L = Length
g = Force of gravity

Answer 5

so you will have to memorise it

Answer 6

I'm not sure what you'll have to do. It depends on the context in which you were taught it i suppose