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A chord of length 64 \mathrm{~m} is used to connect a 100 \mathrm{~kg} astronaut to a spaceship whose mass is much larger than that of the astronaut. Then the value of the tension in the cord. (Assume that the spaceship is orbiting near earth surface. Also assume that the spaceship and the astronaut fall on a straight line from the earth centre. The radius of the earth is 6400 \mathrm{~km}.)
 

Option: 1

2 \times 10^{-2} \mathrm{~N}



 


Option: 2

3 \times 10^{-2} \mathrm{~N}


Option: 3

4 \times 10^{-2} \mathrm{~N}


Option: 4

5 \times 10^{-2} \mathrm{~N}


Answers (1)

best_answer

The tension in the string \mathrm{\mathrm{T}\: is \: given\: as, \mathrm{T}+\mathrm{F}_{\mathrm{gr}}=\mathrm{ma_r}}

\mathrm{ \Rightarrow \mathrm{T}+\frac{\mathrm{GMm}}{(\mathrm{R}+\ell)^2}=\mathrm{m}(\mathrm{R}+\ell) \omega^2 }

\mathrm{ \Rightarrow \mathrm{T}=\mathrm{m}(\mathrm{R}+\ell) \omega^2-\frac{\mathrm{GMm}}{\mathrm{R}^2}\left(\frac{\mathrm{R}}{\mathrm{R}+\ell}\right)^2 }

\mathrm{ \Rightarrow \mathrm{T}=\mathrm{m}(\mathrm{R}+\ell) \frac{\mathrm{g}}{\mathrm{R}}-\mathrm{mg}\left[1+\frac{\ell}{\mathrm{R}}\right]^{-2} }

\mathrm{ \Rightarrow \mathrm{T}=\frac{3 \mathrm{mgl}}{\mathrm{R}}=\frac{3 \times 100 \times 10 \times 64}{6400 \times 10^3}=3 \times 10^{-2} \mathrm{~N} .}

Hence option 2 is correct.




 

Posted by

Ritika Kankaria

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