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Sever21 [200]
3 years ago
13

A newly-discovered planet ("Kardashia") has a mass exactly 4.0 times that of Earth. A particle on the surface of Kardashia has t

he same weight that it would have on the surface of Earth. Determine the radius of Kardashia, in terms of the radius of Earth (RE ).A) .5 REB) 2 REC) 2.5 RED) 3 REE) 3.5 RE
Physics
1 answer:
son4ous [18]3 years ago
3 0

Answer:

r_k=0.5r_e

Explanation:

M_e = Mass of Earth

M_k = Mass of Kardashia = 4M_e

R_e = Radius of Earth

R_k = Radius of Kardashia

Gravitational force of Earth on object

F_e=\frac{GM_em}{r_e^2}

Gravitational force of Kardashia on object

F_k=\frac{GM_km}{r_k^2}\\\Rightarrow F_k=\frac{G4M_e}{r_k^2}

The gravitational force i.e., the weight of the body is same on both the planets

F_e=F_k

If the same particle is used then the mass will also be equal

Dividing the forces

\frac{F_e}{F_k}=\frac{\frac{GM_em}{r_e^2}}{\frac{G4M_e}{r_k^2}}\\\Rightarrow 1=4\frac{r_k^2}{r_e^2}\\\Rightarrow r_k^2=\frac{1}{4}r_1^2\\\Rightarrow r_k=\frac{1}{2}r_e\\\Rightarrow r_k=0.5r_e

The radius of the planet Kardashia is half of the radius of Earth

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