Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of `100 kg` and they are `100 m` apart. They are initially at rest relative to one another. How long will it be before the gravitational attraction brings them `1 cm` closer together?

Options

A. 2.52 days
B. 1.41 days
C. 0.70 day
D. 0.41 day

Answer

B

Explanation

Here `m_(1)=m_(2)=100 kg , r=100 m`
Accelerations of first and second astronauts are
`a_(1)=(Gm_(1)m_(2))/(r^(2))xx(1)/(m_(1))=(Gm_(2))/(r^(2))` and `a_(2)=(Gm_(1)m(2))/(r^(2))xx(1)/(m^(2))=(Gm_(1))/(r^(2))`
Net acceleration of approach
`a=a_(1)+a_(2)=(GM_(2))/(r^(2))+(Gm_(1))/(r^(2))=(2Gm_(1))/(r^(2))`
`=(2xx(6.67xx10^(-11))xx100)/(100)^(2)=2xx6.67xx10^(-13) ms^(-2)`
on solving we get t = 1.41 days