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Q.

The first & second stage of two stage rocket separately weigh 100 kg and 10 kg and contain 800kg and 90kg fuel respectively. If the exhaust velocity of gases is 2 km/sec then final velocity of the rocket after second stage is (nearly) (log₁₀5=0.6990) (neglect gravity)

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a

7.8 × 10³ m/s

b

9.3 × 10³ m/s

c

2.4 × 10³ m/s

d

6.1 × 10³ m/s

answer is A.

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Detailed Solution

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$\begin{array}{l} V = V_{0} + 2.303 \log \frac{m_{0}}{m} \Rightarrow V_{0} = 2.303 \log \frac{m_{0}}{m} \\ = 2.3 \times 2 \times 10^{3} \times \log \frac{1000}{200} \\ = 2.3 \times 2 \times 10^{3} \times 0.6990 = 3.2 \times 10^{3} \\ V = V_{0} + 2.3 \log \frac{m_{0}}{m} \\ = 3.2 \times 10^{3} + 2.3 \times 2 \times 10^{3} \times \log \frac{100}{10} = 7.8 \times 10^{3} m / s \end{array}$

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