Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20249 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2024 · 9 April · Evening Shift · Physics · Gravitation

A satellite of 10^3 ~kg mass is revolving in circular orbit of...

A satellite of 103 kg10^3 \mathrm{~kg} mass is revolving in circular orbit of radius 2R2 R. If 104R6J\frac{10^4 R}{6} J energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use g=10 m/s2,R=g=10 \mathrm{~m} / \mathrm{s}^2, R= radius of earth)

Options

  1. A2.5R2.5 R
  2. B3R3 R
  3. C4R4 R
  4. D6R6 R

Correct answer

D. 6R6 R

Step-by-step solution

 Total energy =−GMm2(2R) if energy =104R6 is added then −GMm4R+104R6=−GMm2r where r is new radius of  revolving and g=GMR2−mgR4+104R6=−mgR22r(m=103kg)−103×10×R4+104R6=−103×10×R22r−14+16=−R2rr=6R\begin{aligned} & \text{ Total energy }=\frac{-\mathrm{GMm}}{2(2 \mathrm{R})} \\ & \text{ if energy }=\frac{10^4 \mathrm{R}}{6} \text{ is added then } \\ & \frac{-\mathrm{GMm}}{4 \mathrm{R}}+\frac{10^4 \mathrm{R}}{6}=\frac{-\mathrm{GMm}}{2 \mathrm{r}} \\ & \text{ where } \mathrm{r} \text{ is new radius\text{ of } revolving and } \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2} \\ & -\frac{\mathrm{mgR}}{4}+\frac{10^4 \mathrm{R}}{6}=-\frac{\mathrm{mgR}^2}{2 \mathrm{r}}\left(\mathrm{m}=10^3 \mathrm{ kg}\right) \\ & -\frac{10^3 \times 10 \times \mathrm{R}}{4}+\frac{10^4 \mathrm{R}}{6}=-\frac{10^3 \times 10 \times \mathrm{R}^2}{2 \mathrm{r}} \\ & -\frac{1}{4}+\frac{1}{6}=-\frac{\mathrm{R}}{2 \mathrm{r}} \\ & \mathrm{r}=6 \mathrm{R}\end{aligned}
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