the period of a pendulum is determined at the equator and again at the North Pole. Will it be the same? Why or why not?
2007-02-04 20:19:39 · 8 answers · asked by somepeoplepleasehelp 2 in Science & Mathematics ➔ Physics
ummm so which one is the right answer?
2007-02-04 20:48:58 · update #1
It won't be the same because g (gravity acceleration) is in fact different when the distance from the center of earth varies, and this is exactly what happens when you get from the equator to the pole (actually the radius decreases in this case).
Dependence of period on gravity is usually given by
T=2π sqrt(l/g), where l is the length of the pendulum
2007-02-04 20:23:43 · answer #1 · answered by supersonic332003 7 · 0⤊ 0⤋
The force of attraction between two masses M1 and M2 is determined by F = M1 X M2 / d^2 where d is the distance between the centers of the two masses. Now in the case of the pendulum, the bob of the pendulum has the mass M1 and earth the much larger mass M2. The acceleration due to gravity is thus inversely proportional to the distance between the two masses. At the equator, the earth's radius is slightly more than at the pole. Hence g is a little smaller and thus the restoring force on the pendulum is less. Thus the period of the pendulum increases. You got the formulas for the time Period from the other answers. So, check it out.
Not only at the pole, but in a deep mine or at the bottom of the sea, a similar thing happens and the Time Period reduces. Conversely, when you take the same pendulum to the top of a mountain or in a rocket, its time period increases.
Hope the concept is clear. The maths is simple once the concept is understood.
2007-02-05 04:50:01 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
No,
The earth is not a perfect sphere, gravitational constant (g) is not the same at the equator and at the north pole.
but I don't think it's going to be too much of a difference.
2007-02-05 04:31:58 · answer #3 · answered by fulbish 2 · 0⤊ 0⤋
No it will not be the same. There will be variation in the observations. This is because of the gravitational force is not same at these two locations.
2007-02-05 04:41:21 · answer #4 · answered by vidhya sagar 2 · 0⤊ 0⤋
yes the period will be the same.
although at the pole, the angle of swing will change constantly (as the earth rotates), so it has to be able to swing at any angle.
2007-02-05 04:32:53 · answer #5 · answered by blu joose 2 · 0⤊ 2⤋
Yeah.
It is independent on where on earth it is placed, except for elevation. It is dependent on gravity.
2007-02-05 04:25:12 · answer #6 · answered by Anonymous · 0⤊ 2⤋
it will be different because value of g is different
t=2pi(l/g)^1/2
2007-02-05 04:25:20 · answer #7 · answered by tarundeep300 3 · 0⤊ 0⤋
yes it will be the same
2007-02-05 04:22:57 · answer #8 · answered by LS 5 · 0⤊ 2⤋