question_answer

A body is suspended from a spring balance kept in a satellite. The reading of the balance is\[{{W}_{1}}\] when the satellite goes in an orbit of radius\[R\] and is\[{{W}_{2}}\]when it goes in an orbit of radius\[2R\]. Which of the following will be correct?

A) \[{{W}_{1}}={{W}_{2}}\]                              

B) \[{{W}_{1}}<{{W}_{2}}\]

C) \[{{W}_{1}}>{{W}_{2}}\]                              

D) \[{{W}_{1}}\ne {{W}_{2}}\]

Correct Answer: A

Solution :

When a body has been suspended from a spring balance in a satellite, then its free body diagram w.r.t. satellite frame of reference is as shown in figure. where,\[R\]is orbital radius of earths satellite and\[v\]is orbital velocity of satellite. Also       \[v=\sqrt{\frac{GM}{R}}\], So, spring force\[=\frac{GMm}{{{R}^{2}}}-\frac{m{{v}^{2}}}{R}=0\] So, whatever be the orbital radius of satellite spring balance reading is zero. So, for given case\[{{W}_{1}}={{W}_{2}}=0\]