Find the escape velocity of a body from the earth. [R(earth) `=6.4xx10^(6)m, rho" (earth)"=5.52xx10^(3)kg//m^(3), G=6.67xx10^(-11)N.m^(2)//kg^(2)]`

Explanation

Data : `R=6.4 xx10^(6)m,`
`rho=5.52xx10^(4=3)kg//m^(3), G=6.67xx10^(-11)N.m^(2)//kg^(2)`
The escape velocity of a body from the earth,
`v_("esc")=2Rsqrt((2)/(3)Gpi rho)`
`=2xx6.4xx10^(6)mxxsqrt((2)/(3)xx6.67xx10^(-11)N.m^(2)//kg^(2)xx3.142xx5.52xx10^(3)kg//m^(3))`
`=1.28xx10^(3)xxsqrt((13.34xx3.142 xx5.52)/(3))`
`=11.24xx10^(3)m//s=11.24km//s`.