The radius of planet A is half the radius of planet B. If the mass of

1.	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 on A?
Answer» Data : R_A = RB/2, gB = \(\frac{1}{2}\) g_A, M_B = ? \(g=\frac{GM}{R^2}\) ∴ g_A= \(\frac{GM_A}{R^{2}_A}\) and g_B= \(\frac{GM_B}{R^2_B}\) ∴ \(\frac{g_B}{g_A}=(\frac{M_B}{M_A})(\frac{R_A}{R_B})^2\) ∴ \(\frac{1}{2}(\frac{M_B}{M_A})(\frac{1}{2})^2\) = \(\frac{1}{4}(\frac{M_B}{M_A})\) ∴ \(\frac{M_B}{M_A}=\frac{4}{2}\) = 2 ∴ M_B = 2M_A.

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 on A?

Answer»

Data : R_A = RB/2, gB = \(\frac{1}{2}\) g_A, M_B = ?

\(g=\frac{GM}{R^2}\)

∴ g_A= \(\frac{GM_A}{R^{2}_A}\) and g_B= \(\frac{GM_B}{R^2_B}\)

∴ \(\frac{g_B}{g_A}=(\frac{M_B}{M_A})(\frac{R_A}{R_B})^2\)

∴ \(\frac{1}{2}(\frac{M_B}{M_A})(\frac{1}{2})^2\) = \(\frac{1}{4}(\frac{M_B}{M_A})\)

∴ \(\frac{M_B}{M_A}=\frac{4}{2}\) = 2

∴ 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 on A?

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