Step 1: Understand the formula for escape velocity, which is v = √(2GM/R). Here, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
Step 2: Identify the values given in the question. The radius of the planet is 4R and the mass is 2M.
Step 3: Substitute the values into the escape velocity formula. Replace M with 2M and R with 4R in the formula: v = √(2G(2M)/(4R)).
Step 4: Simplify the expression inside the square root. This gives us v = √(4GM/4R).
Step 5: Further simplify the expression. The 4 in the numerator and denominator cancels out, resulting in v = √(GM/R).
Step 6: Now, we need to multiply the original escape velocity formula by 2 to account for the mass being 2M. This gives us v = √(2 * 2GM/4R) = √(8GM/4R).
Step 7: Finally, simplify the expression again to get v = √(8GM/R).
