Question:

A particle is projected with a velocity so that height attained becomes equal to the radius of the earth. Then the velocity is

Updated On: May 12, 2024
  • $\sqrt{\frac{GM}{R}}$
  • $\sqrt{\frac{2GM}{R}}$
  • $\sqrt{\frac{8GM}{R}}$
  • $\frac{GM}{R}$
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The Correct Option is A

Solution and Explanation

Answer (a) $\sqrt{\frac{GM}{R}}$
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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].