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A satellite of mass 100 kg performs unif...

A satellite of mass 100 kg performs uniform circular motion around the earth at a height of 6400 km from the earth's surface. Find the gravitational potential energy.
`[g=9.8m//s^(2), R=6400km]`

Text Solution

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Data : `m=100kg, g=9.8m//s^(2)`,
`R=6400km=6.4xx10^(6)m, h=6.4xx10^(6)m`
The gravitational potential energy of the satellite
`=-(GMm)/(R+h)=-(mgR^(2))/(R+h)" "(because g=(GM)/(R^(2)))`
`=-(100kg xx9.8m//s^(2)xx(6.4xx10^(6)m)^(2))/((6.4xx10^(6)+6.4xx10^(6))m)`
`=-(9.8xx6.4xx6.4xx10^(14))/(2xx6.4xx10^(6))J=-9.8xx3.2xx10^(8)J`
`=-3.136xx10^(9)J.`
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Knowledge Check

  • The earth is a solid sphere of radius 6400 km, the value of acceleration due to gravity at a height 800 km above the surface of the earth is

    A
    `5.35m//s^(2)`
    B
    `6.35m//s^(2)`
    C
    `7.35m//s^(2)`
    D
    `8.35m//s^(2)`

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