Question:

The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value of A?

Answer:

Suppose the radius of planet A= R_A And radius of planet B = R_B And

Mass of planet A = M_A, then find mass of planet B = M_B.

Here, R_A= R_B/2, g_B= ½ g_A

Then, g= GM / R₂ And g_A = GM_A /R²_A

Therefore, g_B = G M_B/ R²_B

Now, M_B/ R²-B = ½ [GM_A /(R_B/2)²]

M_B/ R²_B= ½ [4 (GM_A /(R_B)²)]

So, M_B= 2M_A

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The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value of A?

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