Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202621 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2026 · 21 January · Morning Shift · Physics · Gravitation

Initially a satellite of 100 kg is in a circular orbit of radius...

Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE1.5 \mathrm{R}_{\mathrm{E}}. This satellite can be moved to a circular orbit of radius 3RE3 R_{E} by supplying α×106 J\alpha \times 10^{6} \mathrm{~J} of energy. The value of α\alpha is ____\_\_\_\_. (Take Radius of Earth RE=6×106 mR_{E}=6 \times 10^{6} \mathrm{~m} and g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2})

Options

  1. A150
  2. B1000
  3. C500
  4. D100

Correct answer

B. 1000

Step-by-step solution

Total energy of satellite in orbit: E=−GMm2r=−gRE2m2rE = -\frac{GMm}{2r} = -\frac{gR_E^2 m}{2r}
E1=−gRE2m2(1.5RE)=−gREm3E_1 = -\frac{gR_E^2 m}{2(1.5R_E)} = -\frac{gR_E m}{3}
E2=−gRE2m2(3RE)=−gREm6E_2 = -\frac{gR_E^2 m}{2(3R_E)} = -\frac{gR_E m}{6}
Energy supplied =E2−E1=−gREm6+gREm3=gREm6= E_2 - E_1 = -\frac{gR_E m}{6} + \frac{gR_E m}{3} = \frac{gR_E m}{6}
=10×6×106×1006=109= \frac{10 \times 6 \times 10^6 \times 100}{6} = 10^9 J =1000×106= 1000 \times 10^6 J
α=1000\alpha = 1000
Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum ℓ is moving in a circular orbit of radius r_0… JEE Advanced 2026A body of mass m is taken from the surface of earth to a height equal to twice the radius… JEE Main 2026When one moves from a point 16 km below the earth's surface to a point 16 km above the… JEE Main 2026The height in terms of radius of the earth (R) , at which the acceleration due to gravity… JEE Main 2026If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and… JEE Main 2026A planet (P_1) is moving around the star of mass 2M in the orbit of radius R . Another… JEE Main 2026Three masses 200 ~kg, 300 ~kg and 400 kg are placed at the vertices of an equilateral… JEE Main 2026Given below are two statements: Statement I : A satellite is moving around earth in the… JEE Main 2026 Full Gravitation list All JEE Main PYQs