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Question: Two identical solid copper spheres of radius R are placed in contact with each other. The gravitatio...

Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to
A.R2{R^2}
B.R−2{R^{ - 2}}
C.R−4{R^{ - 4}}
D.R4{R^4}

Explanation

Solution

We need to know that the states of matter are mainly divided into three types and that is, solid, liquid and gas. And each matters have different chemical and physical properties. In solids, all the particles are arranged very closely. Hence, the force of attraction present between the particles is very strong and it cannot be moved and it has a definite shape. And the solids are mainly divided into four types and that is, ionic solids, molecular solids, metallic solids and network covalent solids.

Complete answer:
The gravitational attraction between them is not proportional toR2{R^2}. Hence, option (A) is incorrect.
The gravitational force present between two copper spheres is not proportional toR−2{R^{ - 2}}. Hence, option (B) is incorrect.
The gravitational attraction between them is not proportional toR−4{R^{ - 4}}. Hence, option (C) is incorrect.
According to the question, here two identical solid copper spheres of radius R are placed in contact with each other.
The mass of each copper sphere, M1=M2=ρ(43πR3){M_1} = {M_2} = \rho \left( {\dfrac{4}{3}\pi {R^3}} \right)
The formula of gravitational force, F can be written as,
F=G(M1)(M2)(2R)2F = \dfrac{{G\left( {{M_1}} \right)\left( {{M_2}} \right)}}{{{{\left( {2R} \right)}^2}}}
Substitute the value of M1{M_1}and M2{M_2}in the above equation.
F=Gρ(43πR3)ρ(43πR3)4R2=49π2Gρ2R4F = \dfrac{{G\rho \left( {\dfrac{4}{3}\pi {R^3}} \right)\rho \left( {\dfrac{4}{3}\pi {R^3}} \right)}}{{4{R^2}}} = \dfrac{4}{9}{\pi ^2}G{\rho ^2}{R^4}
Therefore, we can say that the gravitational force present between two copper spheres is proportional to the fourth power of radius.

Hence, option (D) is correct.

Note:
We have to know that copper is used as a good conductor of electricity and it is used as a stimulation of energy. The copper sphere is mainly used for decorative purposes and it is also used for cleaning rituals and healing. The copper is also known as lucky metal or healing metal. If two identical solid copper spheres are connected with each other, then the gravitational force is proportional to the fourth power of radius.