Maharashtra State BoardHSC Science (General) 11th

Answer the following question in detail. Show that acceleration due to gravity at height h above the Earth’s surface is gh=g(RR + h)2 and Discuss the variation of acceleration due to - Physics

Advertisement Remove all ads
Answer in Brief

Answer the following question in detail.

Show that acceleration due to gravity at height h above the Earth’s surface is `"g"_"h" = "g"("R"/"R + h")^2`

Answer the following question in detail.

Discuss the variation of acceleration due to gravity with altitude.

Advertisement Remove all ads

Solution

  1. Let,
    R = radius of the Earth,
    M = mass of the Earth.
    g = acceleration due to gravity at the surface of the Earth.
  2. Consider a body of mass m on the surface of the Earth. The acceleration due to gravity on the Earth’s surface is given by,
    `"g" = "GM"/"R"^2`     ....(1)
  3. The body is taken at height h above the surface of the Earth as shown in the figure. The acceleration due to gravity now changes to,
    `"g"_"h" = "GM"/("R + h")^2`     .....(2)
  4. Dividing equation (2) by equation (1), we get,
    `"g"_"h"/"g" = ("GM"/("R + h")^2)/("GM"/"R"^2)`
    `therefore "g"_"h"/"g" = "R"^2/("R + h")^2`
    `therefore "g"_"h" = "gR"^2/("R + h")^2`
    We can rewrite,
    `therefore "g"_"h" = "gR"^2/("R"^2(1 + "h"/"R")^2)`
    `therefore "g"_"h" = "g"(1 + "h"/"R")^-2`
  5. For small altitude h, i.e., for `"h"/"R"` << 1, by neglecting higher power terms of `"h"/"R"`, `"g"_"h" = "g"(1 - "2h"/"R")`

This expression can be used to calculate the value of g at height h above the surface of the Earth as long as h << R.

Concept: Variation in the Acceleration Due to Gravity with Altitude, Depth, Latitude and Shape
  Is there an error in this question or solution?

APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 5 Gravitation
Exercises | Q 3. (iii) | Page 98
Balbharati Physics 11th Standard Maharashtra State Board
Chapter 5 Gravitation
Exercises | Q 3. (xvi) | Page 98
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×