If the mass of a planet is doubled with no increase in its size,the escape speed for that planet is
A)increased by a factor of 1.4.
B)increased by a factor of 2.
C)not changed.
D)reduced by a factor of 1.4.
E)reduced by a factor of 2.

Question

Quizplus · Accepted Answer

The escape speed $v_e$ from a planet is given by the formula $v_e = \sqrt{\frac{2GM}{R}}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is the radius of the planet. If the mass of the planet is doubled ($M$ becomes $2M$), the escape speed becomes $\sqrt{\frac{2G(2M)}{R}} = \sqrt{2} \times \sqrt{\frac{2GM}{R}}$, which is $\sqrt{2}$ times the original escape speed. Since $\sqrt{2}$ is approximately 1.4, the escape speed is increased by a factor of 1.4.

If the Mass of a Planet Is Doubled with No