Physics, asked by amanshafi72, 1 day ago

find the value of g on the surface of planet whose mass is thrice as that of earth and radius is twice as that of earth​

Answers

Answered by Yuseong
42

Given :

  • A planet's mass is thrice as that of earth.
  • And, radius is twice as that of earth.

To find :

  • Value of g on the surface of planet.

___________________________________________

If Earth's mass is m and its radius is r. So, acceleration due to gravity on its surface is given by,

   \quad \twoheadrightarrow\boxed{\sf {\purple{ g = G\dfrac{m}{r^2} }}} \\

  • G denotes acceleration due to gravity
  • m denotes mass
  • r denotes radius

Now, as the planet's mass is thrice as that of earth and radius is twice as that of earth. So,

  • Planet's mass = 3m
  • Planet's radius = 2r

Now, acceleration due to gravity on the surface of the planet will be given by,

   \quad \twoheadrightarrow\sf { g_P = G\dfrac{3m}{(2r)^2}} \\

   \quad \twoheadrightarrow\sf { g_P= G\dfrac{3m}{4r^2}} \\

   \quad \twoheadrightarrow\sf { g_P= \dfrac{3}{4}G\dfrac{m}{r^2}} \\

   \quad \twoheadrightarrow\boxed{\sf { g_P= \dfrac{3}{4}g }} \\

Therefore, the value of g on the surface of planet ¾th of the value of g on the earth

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