question_answer

A chord of length 90 m is used to tie a 200 kg astronaut (with his space suit and instruments) with his spaceship. Tension in the chord is nearly

A) 0.0084 N

B) 0.084 N

C) 0.84 N

D) 8.40 N

Correct Answer: B

Solution :

Let angular speed of spaceship and astronaut is co.

Forces on astronaut provides necessary centripetal pull.

\[\Rightarrow \]\[\frac{G{{M}_{e}}m}{{{(r+L)}^{2}}}+T=m(r+L){{\omega }^{2}}\]

\[\Rightarrow \]\[mg{{\left( 1-\frac{L}{r} \right)}^{2}}+T=\frac{mg}{r}(r+L)\]

Taking \[r=R\](radius of earth)

\[\Rightarrow \]\[mg-\frac{2mgL}{R}+T=mg+\frac{mgL}{R}\]

\[\Rightarrow \]\[T=\frac{3mgL}{R}=\frac{3\times 200\times 10\times 90}{6400\times {{10}^{3}}}=0.084N\]