Question

assume that the mass of the earth is 100 times larger than the mass of the moon and radius of Earth is 4 times that of moon . show that the weight of an object is about 1/6 of that on earth. THE GUY WHO WILL GIVE ANSWER WITH EXPLANATION WILL BE MARKED AS BRAINLIST

Answer 1

heres you answer.... click on the photo to get full answer

Answer 2

Given :

Mass of earth ($M_E$) = 100 × Mass of moon ($M_m$)

Radius of earth ($R_E$) = 4 × Radius of the moon ($R_m$)

To Find :

To prove the weight of an object on moon is about 0.16  of that on earth.

Solution :

Acceleration due to gravity on the earth's surface (g) = $\frac{GM_E}{(R_E)^2}$

                                                                                        = $\frac{G*100M_m}{(4R_m)^2}$

Acceleration due to gravity on the moon's surface (g') = $\frac{GM_m}{(R_m)^2}$    

Let the mass of the object be 'M'

Weight of the object on earth (W) = M × g

                                                        = M × $\frac{G*100M_m}{(4R_m)^2}$

                                                        = M × $\frac{100GM_m}{16R_m^2}$

Weight of the object on moon (W') = M × $\frac{GM_m}{(R_m)^2}$      

       $\frac{W}{W'} = \frac{\frac{M*100GM_m}{16R_m^2}}{\frac{M*GM_m}{(R_m)^2}}$

⇒   $\frac{W}{W'}$   =  $\frac{100}{16}$

⇒ W'    =  0.16 W

Therefore, weight of the object on moon is 0.16 times that of weight of the object on earth,

Hence proved.

Note :

The question given is wrong. It should be this -

Assume that the mass of the earth is 100 times larger than the mass of the moon and radius of Earth is 4 times that of moon . show that the weight of an object is about 0.16 of that on earth.