The escape velocity of a body from the surface of the earth depends upon (i) the mass of the earth M, (ii) The radius of the eath R, and (iii) the gravitational constnat G. Show that v=ksqrt((GM)/R), using the dimensional analysis.

The escape velocity of a body from the surface of the earth depends up

1.	The escape velocity of a body from the surface of the earth depends upon (i) the mass of the earth M, (ii) The radius of the eath R, and (iii) the gravitational constnat G. Show that v=ksqrt((GM)/R), using the dimensional analysis.
Answer» Solution :`V=kG^(x)M^(y)R^(Z),[LT^(-1)]=[M^(-1)L^(3)T^(-2)]^(x)M^(y)L^(z)`. SIMPLIFYING `x=1//2, M=-1//2, z=-1//2`.