Question

Derive a mathematical expression to find the weight of an object on moon in comparison with that on earth .

I will make you brainlist....​

Answer 1

Answer:

weight of body on moon is 1\6 times its wieght on earth

Answer 2

Answer:

The weight of the moon is $1/6$ that of the earth.

Explanation: To derive a mathematical expression to find the weight of an object on moon in comparison with that on earth .

Let,

Consider a body of mass "$m$" and weight "$W_{m}$" on the moon.

The moon has a mass of "$M$" and a radius of "$R$."

Weight of an object on the moon = Force with which the moon pulls.

$W_{m}=G\frac{Mm}{R^{2} }$

The identical thing weighs $W_{e}$ when it is placed on earth.

The earth's mass is $100$ times greater than that of the moon.

Radius of the moon $= R$

Radius of the Earth $= 4R$

the object's weight relative to the earth$=W_{e}=G\frac{100Mm}{(4R)^{2} }$

$=W_{e}=G\frac{100Mm}{16R^{2} }$

$\frac{W_{m} }{W_{e} }=\frac{G\frac{Mn}{R^{2} } }{G\frac{100Mn}{16R^{2} } }=\frac{16}{100}\approx\frac{1}{6}$

As a result, the weight of the moon is $1/6$ that of the earth.

For more similar questions refer to-

https://brainly.in/question/5448087

https://brainly.in/question/767033

#SPJ3