Question

The escape velocity on earth is 11.2 km / s what will be its value on a planet having double the radius and eight times the mass of earth

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

Answer 2

2 times of 11.2

2*11.2 =22.4

as the formula is (2GM/R)^1/2