A small asteroid of mass moves directly towards a planet of mass

PHYSICS · Single correct · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A small asteroid of mass

m

moves directly towards a planet of mass

M

. Its speed is

v_{0}

when it is at a distance

5R

from the planet’s centre (

R

is the planet’s radius). Neglect all forces except the planet’s gravity. Which expression gives its speed

v

when it reaches a distance

2R

from the planet’s centre? (a)

v^{2}=v_{0}^{2}+\dfrac{5GM}{3R}

(b)

v^{2}=v_{0}^{2}+\dfrac{3GM}{5R}

(c)

v^{2}=v_{0}^{2}+\dfrac{7GM}{5R}

(d)

v^{2}=v_{0}^{2}+\dfrac{3GM}{10R}