Question

if the mass of a planet is half of the mass of the earth and of the same radius as earth then compute the value of acceleration due to gravity on that planet​

Answer 1

QUESTION-:

if the mass of a planet is half of the mass of the earth and of the same radius as earth then compute the value of acceleration due to gravity on that planet​

EXPLANATION-:

We know-:

Acceleration due to gravity on earth-:

$\longrightarrow \boxed{\bf\;g=\frac{Gm_e}{R_e^2}}\bf\;=9.8\;m/s^2$

Where-:

$\sf\;m_e=mass\;of\;earth\\\\\sf\;R_e=radius\; of\; earth$

And the acceleration on the planet will be-:

$\bf\; g_p=\frac{Gm_p}{R_p^2}$

Since the mass is half of the planet of the earth we have-:

$\bf\; g_p=\frac{G(m_e/2}{R_e^2}\;\;\;(R_e=R_p)\\\\\bf\; g_p=\frac{Gm_e(1/2)}{R_p^2}\\\\\b\f; g_p=g\times \frac{1}{2}\\\\\bf\; g_p=g/2\\\\\bf\; g_p=9.8/2\\\\\\\bf\; g_p=4.9 \;m/s^2$

So the value of g is 4.9 m/s²

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