Question

Two astronauts each have a mass of $75.0\text{kg}$ are connected by a $10.0\text{m}$ long rope of negligible mass. They are isolated in space and orbit around common centre of mass with a speed of $10.0\text{m/s}$ relative to each other, as shown in figure.

• A. Tension in the string will be $375\text{N}$
• B. Tension in the string will be $1500\text{N}$
• C. Acceleration of astronaut will be $5{\text{m/s}}^2$
• D. Acceleration of astronaut will be $20{\text{m/s}}^2$

Answer 1

Answer: (A), (C)

The correct options are
A Tension in the string will be $375\text{N}$
C Acceleration of astronaut will be $5{\text{m/s}}^2$

Let $u$ be speed of the astronaut
Given speed of astronauts relative to one another $10\text{m/s}$
Relative speed $=u-(-u)=2u=10\Rightarrow u=5\text{m/s}$

for circular motion
$T=\frac{m{u}^2}{R}=\frac{75\times 25}{5}=375\text{N}$
Acceleration of the astronaut$=\frac{v^2}{R}=\frac{25}{5}=5{\text{m/s}}^2$