A) \[{{T}_{st}}>{{T}_{ma}}\]
B) \[{{T}_{ma}}>{{T}_{st}}\]
C) \[{{T}_{sp}}<{{T}_{is}}\]
D) \[{{T}_{st}}={{T}_{ma}}={{T}_{sp}}={{T}_{is}}\]
Correct Answer: C
Solution :
(i) \[{{T}_{st}}=2\pi \sqrt{\frac{{{(R+h)}^{3}}}{GM}}\]\[=2\pi \sqrt{\frac{R}{g}}\] [As h <<R and \[GM=g{{R}^{2}}]\] (ii) \[{{T}_{ma}}=2\pi \sqrt{\frac{R}{g}}\] (iii) \[{{T}_{sp}}=2\pi \sqrt{\frac{1}{g\left( \frac{1}{l}+\frac{1}{R} \right)}}=2\pi \sqrt{\frac{R}{2g}}\] [As l = R] (iv) \[{{T}_{is}}=2\pi \sqrt{\frac{R}{g}}\] \[[As\,\,l=\infty ]\]You need to login to perform this action.
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