Verified Solution • 2025–26 Session moderate

Q7.17: NCERT Physics - Part 1 GRAVITATION 7.17 Solution: A rocket is fired vertically with a speed of 5 km/s from the…

A rocket is fired vertically with a speed of 5 km/s from the earth's surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth =6.0×1024= 6.0 \times 10^{24} kg; mean radius of the earth =6.4×106= 6.4 \times 10^6 m; G=6.67×10−11G = 6.67 \times 10^{-11} N m_ kg__.

Step-by-Step Verified Solution

**Answer:** 1.6×1061.6 \times 10^6 m from the Earth's surface. **Step-by-Step Explanation:** Using conservation of energy:
12mv2−GMmR=−GMmR+h\frac{1}{2}mv^2 - \frac{GMm}{R} = -\frac{GMm}{R+h}
12v2=GM(1R−1R+h)=GMhR(R+h)\frac{1}{2}v^2 = GM\left(\frac{1}{R} - \frac{1}{R+h}\right) = \frac{GMh}{R(R+h)}
With v=5×103v = 5 \times 10^3 m/s:
h=v2R22GM−v2R=(5×103)2(6.4×106)22(6.67×10−11)(6×1024)−(5×103)2(6.4×106)=1.6×106 mh = \frac{v^2 R^2}{2GM - v^2 R} = \frac{(5 \times 10^3)^2 (6.4 \times 10^6)^2}{2(6.67 \times 10^{-11})(6 \times 10^{24}) - (5 \times 10^3)^2(6.4 \times 10^6)} = 1.6 \times 10^6 \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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