Correct Answer  Option 2 :
\(\frac{v}{\sqrt 6}\)
Concept:
Escape Velocity (v):
V = √(2gR)  (1)
Calcuation:
We know that the acceleration due to gravity on the planet is onesixth of acceleration due to gravity on Earth.
So, acceleration due to the gravity of the planet is onesixth as that of
\(g' = \frac{g}{6}\)  (2)
So, Escape velocity on that planet is given as
v' = √(2g'R)  (3)
Radius is Same
Now, putting (2) in (3)
\(v' = \sqrt {2\frac{g'}{6}.r} = \frac{\sqrt {2gr}}{\sqrt{6}}\)
Putting (1) in above equation
\(\implies v' = \frac{v}{\sqrt 6}\)
So, the correct option is \(\frac{v}{\sqrt 6}\)

Gravitational Potential Energy: The potential energy is energy stored in an object by going against the gravity of the earth.
 The gravitational potential energy due to earth is
\(U = \frac{GMm}{R}\)
 For escaping the earth's gravitational influence the kinetic energy should overcome this potential energy. The kinetic energy is given as
\(K = \frac{1}{2}mv^2\)
 For the body to escape earth's gravity,
\(\frac{1}{2}mv^2 = \frac{GMm}{R}\)
⇒ \(v = \sqrt{\frac{2GM}{R}}\)
R is the radius of the earth, M is the mass of earth, G is the universal gravitational constant.