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Question

The moon's radius is $$1/4$$ times that of the earth and its mass $$1/80$$ times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is :


A
g/4
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B
g/5
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C
g/6
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D
g/8
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Solution

The correct option is B $$g/5$$
Acceleration due to gravity on the earth's surface is $$g=\dfrac{GM_e}{R_e^2}$$
Acceleration due to gravity on the moon's surface is $$g_m=\dfrac{GM_m}{R_m^2}$$
Given, $$R_m=\dfrac{R_e}{4}$$ or $$\dfrac{R_m}{R_e}=\dfrac{1}{4}$$ and $$M_m=\dfrac{M_e}{80}$$ or $$\dfrac{M_m}{M_e}=\dfrac{1}{80}$$
So, $$\dfrac{g_m}{g}=\dfrac{M_m}{M_e}\times (\dfrac{R_e}{R_m})^2=(1/80)\times (4)^2=1/5$$
or $$g_m=g/5$$

Physics

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