Question

The radius and acceleration due to
gravity of moon are 1/4 and 1/5 that of
earth. The ratio of the mass of earth
to mass of moon is
1) 1:80 2) 80:1 3) 1:20 4)20:1​

Answer 1

Answer:

2nd option is the right option

Answer 2

The ratio of the mass of earth  to mass of moon is 20:1.

(4) is correct option

Explanation:

Given that,

Radius of moon $r_{m}=\dfrac{1}{4}r_{e}$

Acceleration of moon $g_{m}=\dfrac{1}{5}g_{e}$

We need to calculate the ratio of the mass of earth  to mass of moon

Using formula of gravity

$g =\dfrac{GM}{r}$

For moon,

$g_{m}=\dfrac{GM_{m}}{r_{m}}$...(I)

For earth,

$g_{e} =\dfrac{GM_{e}}{r_{e}}$....(II)

Dividing equation (II) by equation (I)

$\dfrac{g_{e}}{g_{m}}=\dfrac{\dfrac{GM_{e}}{r_{e}}}{\dfrac{GM_{m}}{r_{m}}}$

$\dfrac{g_{e}}{\dfrac{1}{5}g_{e}}=\dfrac{M_{e}r_{m}}{r_{e}M_{m}}$

$\dfrac{5g_{e}}{g_{e}}=\dfrac{M_{e}}{4M_{m}}$

$\dfrac{M_{e}}{M_{m}}=\dfrac{20}{1}$

Hence, The ratio of the mass of earth  to mass of moon is 20:1.

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Topic : acceleration

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