Question:
The time period of a simple pendulum at the centre of the earth is
The time period of a simple pendulum at the centre of the earth is
Updated On: Aug 15, 2022
- zero
- infinite
- less than zero
- none of these
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The Correct Option is B
Solution and Explanation
Acceleration due to gravity at the center of the earth is zero.
$
\Longrightarrow g =0
$
Time period of a simple pendulum is given by,
$T =2 \pi \sqrt{\frac{1}{ g }}$
$
\Longrightarrow T =2 \pi \sqrt{\frac{1}{0}} \\
\therefore T =\infty
$
So time period at the centre of the earth becomes infinite.
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].