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Calculate the critical velocity (v(c))...

Calculate the critical velocity `(v_(c))` of the satellite to be located at 35780 km above the surface of the earth .

Text Solution

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Given : ` G = 6.67 xx 10^(-11) N.m^(2)//kg^(2)`
M (Earth) = `6 xx 10^(34)` kg, R (Earth) = ` 6.4 xx 10^(6) m`
h : 35780 km = ` 3578- x 10^(3) m, v_(c) = ? `
Ciritial velocity of the satellite
` v_(c) = sqrt((GM)/(R+h))`
`sqrt((6.67 xx 10^(-11)N.m^(2) kg^(2)xx6xx10^(24)kg)/(6.4 xx 10^(6) m + 35780 xx 10^(3)m))`
` sqrt((400200xx10^(6))/42180) m//s " " therefore sqrt(9.488) xx 10^(3) ` m/s
` 3.08 xx 10^(3)` m/s = 3.08 km/s
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