Gravitation

JEE Main level, single correct, medium

166 of 223

Question 166 of 223

Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE1.5 \mathrm{R}_{\mathrm{E}}. This satellite can be moved to a circular orbit of radius 3RE3 R_{E} by supplying α×106 J\alpha \times 10^{6} \mathrm{~J} of energy. The value of α\alpha is ____\_\_\_\_. (Take Radius of Earth RE=6×106 mR_{E}=6 \times 10^{6} \mathrm{~m} and g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2})

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Answer: (B) 1000

Total energy of satellite in orbit: E=−GMm2r=−gRE2m2rE = -\frac{GMm}{2r} = -\frac{gR_E^2 m}{2r}
E1=−gRE2m2(1.5RE)=−gREm3E_1 = -\frac{gR_E^2 m}{2(1.5R_E)} = -\frac{gR_E m}{3}
E2=−gRE2m2(3RE)=−gREm6E_2 = -\frac{gR_E^2 m}{2(3R_E)} = -\frac{gR_E m}{6}
Energy supplied =E2−E1=−gREm6+gREm3=gREm6= E_2 - E_1 = -\frac{gR_E m}{6} + \frac{gR_E m}{3} = \frac{gR_E m}{6}
=10×6×106×1006=109= \frac{10 \times 6 \times 10^6 \times 100}{6} = 10^9 J =1000×106= 1000 \times 10^6 J
α=1000\alpha = 1000

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