Question:
The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become
The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become
Updated On: Jan 18, 2023
- 10 hours
- 80 hours
- 40 hours
- 20 hours
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The Correct Option is C
Solution and Explanation
Time period of a satellite is the time taken by satellite to go once around the earth. $T =2 \pi \sqrt{\frac{ r ^{3}}{ MG }}$,
so $T$ depends on $r ^{\frac{3}{2}}$.
so if $r$ is increased to $4$ times then time period will be $8$ times
$\left(4^{\frac{3}{2}}=8\right)$.
so $T$ depends on $r ^{\frac{3}{2}}$.
so if $r$ is increased to $4$ times then time period will be $8$ times
$\left(4^{\frac{3}{2}}=8\right)$.
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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].