Question

seharitat -The distance of a panet from the earth is 2.5 x 10^7 km and the gravitational force between them them is 3.82 x 10^18 N. Mass of the planet and earth are equal, each being 5.98 x 10^24 Kg. Calculate the universal gravitation constant.​

Answer 1

• F=3.82×10^18N
• Mass of earth=M=5.98×10^24kg
• Mass of planet=m=5.98×10^24kg
• Distance=r=2.5×10^7km

• Universal gravitation constant=G

We know

`\boxed{\sf F=G(Mm)/(r^2)}`

`\\ \sf\longmapsto G=(Fr^2)/(Mm)`

`\\ \sf\longmapsto G=(3.82* 10^(18)(2.5* 10^7)^2)/((5.98* 10^(24))^2)`(M=m)

`\\ \sf\longmapsto G=(3.82* 10^(18)(6.25* 10^(14)))/(35.7* 10^(48))`

`\\ \sf\longmapsto G=(23.87* 10^(32))/(35.7* 10^(48))`

`\\ \sf\longmapsto G=0.668*10^(-16)`

`\\ \sf\longmapsto G=6.68* 10^(-15)`