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NEET-XII-Physics
11: Gravitation
- #34What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?Ans : For a geostationary satellite, we have:
R = 6.4 × 103 km
h = 3.6 × 103 km
Given: mg = 10 N
The true weight of the object in the geostationary satellite is given by
`` mg\text{'}=mg-\frac{{R}^{2}}{{\left(R+h\right)}^{2}}``
`` =10-\frac{{\left(6400\times {10}^{3}\right)}^{2}}{\left(6400\times {10}^{3}+3600\times {10}^{3}\right)}``
`` =10-\left[\frac{{\left(64\times {10}^{5}\right)}^{2}}{\left(6.4\times {10}^{6}+36\times {10}^{5}\right)}\right]``
`` =10-\left[\frac{4096\times {10}^{10}}{{\left(42.4\right)}^{2}\times {10}^{12}}\right]``
`` =\frac{4096}{17980}=0.227\,\mathrm{\,N\,}``
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