Verified Solution • 2025–26 Session moderate

Q7.12: NCERT Physics - Part 1 GRAVITATION 7.12 Solution: A rocket is fired from the earth towards the sun. At what…

A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero? Mass of the sun =2×1030= 2 \times 10^{30} kg, mass of the earth =6×1024= 6 \times 10^{24} kg. Neglect the effect of other planets etc. (orbital radius =1.5×1011= 1.5 \times 10^{11} m).

Step-by-Step Verified Solution

**Answer:** At a distance of 2.6×1082.6 \times 10^8 m from the Earth's centre. **Step-by-Step Explanation:** Let the distance from Earth be xx, then distance from Sun is (1.5×1011−x)(1.5 \times 10^{11} - x). For gravitational force to be zero:
GMEx2=GMS(1.5×1011−x)2\frac{GM_E}{x^2} = \frac{GM_S}{(1.5 \times 10^{11} - x)^2}
6×1024x2=2×1030(1.5×1011−x)2\frac{6 \times 10^{24}}{x^2} = \frac{2 \times 10^{30}}{(1.5 \times 10^{11} - x)^2}
(1.5×1011−x)2x2=2×10306×1024=3.33×105\frac{(1.5 \times 10^{11} - x)^2}{x^2} = \frac{2 \times 10^{30}}{6 \times 10^{24}} = 3.33 \times 10^5
1.5×1011−xx=577\frac{1.5 \times 10^{11} - x}{x} = 577
x=1.5×1011578=2.6×108 mx = \frac{1.5 \times 10^{11}}{578} = 2.6 \times 10^8 \text{ m}

All Questions in this Chapter

Q7.1 Q7.2 Q7.3 Q7.4 Q7.5 Q7.6 Q7.7 Q7.8 Q7.9 Q7.10 Q7.11 Q7.12 Q7.13 Q7.14 Q7.15 Q7.16 Q7.17 Q7.18 Q7.19 Q7.20 Q7.21

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