Question

If the escape velocity on earth is 11.2 km/sec, its value for a planet having double the radius and 8 times the mass of earth is .............. m/s.

Answer 1

for earth escape velocity of earth is calucated by taking kinetic energy at surface equal to potential energy at infinty and as we know potential enegy at infinity for solid sphere like earth which results in ve = (2GM/R)∧1/2

Now after comparing with the planet given M'=8M ,R'=2R

therefore new v=(2GM'/R')∧1/2

v = (2G*8M/2R)∧1/2=(2GM*4/R)∧1/2 = 2(2GM/R)∧1/2 = 2ve (from above) = 11.2 *2 =22.4