A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth

A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is( g is acceleration due to gravity on the surface of earth)

Options

(a) (GM / R)¹/²
(b) (GM / 2R)¹/²
(c) (GR / 4)¹/²
(d) (2G / 4)¹/²

Correct Answer:

(GM / 2R)¹/²

Explanation:

As we know, the minimum speed with which a body is projected so that it doe snot return back is called escape speed.
vₑ = √(2GM / r) = √(2GM / R + h) = √(2GM / 4R)
= (GM / 2R)¹/² ( h = 3R)

admin:

View Comments (1)

Related Questions

  1. A tuning fork vibrates with 2 beats in 0.04 second. The frequency of the fork is
  2. An alternating electric field, of frequency v, is applied across the dees (radius = R)
  3. Two bulbs 60 W and 100 W designed for voltage 220 V are connected in series
  4. A solid which is transparent to visible light and whose conductivity increases
  5. The nuclear radius of a certain nucleus is 7.2 fm and it has a charge of 1.28×10⁻¹⁷ C.