1. Use the formula for escape velocity

   The escape velocity from the surface of a planet is $v_e = \sqrt{\frac{2GM}{R}}$ where:

   • $G$ is the gravitational constant,
   • $M$ is the mass of the planet,
   • $R$ is the radius of the planet.

2. Write the ratio of escape velocities

   Let:

   • mass of Earth $= M_E$,
   • radius of Earth $= R_E$.

   Given for the planet: $M_P = 16M_E, \qquad R_P = 4R_E$

   Then $\frac{v_P}{v_E} = \sqrt{\frac{2GM_P/R_P}{2GM_E/R_E}}$

   Cancelling $2G$: $\frac{v_P}{v_E} = \sqrt{\frac{M_P/R_P}{M_E/R_E}}$

3. Substitute the given values

   $\frac{v_P}{v_E} = \sqrt{\frac{16M_E/(4R_E)}{M_E/R_E}}$

   $= \sqrt{\frac{16}{4}} = \sqrt{4} = 2$

4. Hence the ratio

   $v_P : v_E = 2 : 1$

5. Check options

   • A: $1:4$ ❌
   • B: $1:\sqrt{2}$ ❌
   • C: $4:1$ ❌
   • D: $2:1$ ✅

Therefore, the correct answer is D.