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Q.

A rocket consumes 20 kg fuel per second. The exhaust gases escape at a speed of 1000 ms^–1 relative to the rocket. Calculate the upthrust received by the rocket. Also calculate the velocity acquired when its mass is 1/100 of the initial mass.

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a

2 × 10⁴ N ; 4.6 Km

b

2 × 10⁶ N ; 5.3 Km/s

c

4 × 10² N ; 4.6 Km/s

d

4 × 10⁶ N ; 5.3 Km/s

answer is A.

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Detailed Solution

$\begin{array}{l} F = \frac{{mv}_{r}}{t} = 20 \times 1000 = 2 \times 10^{4} N \\ V = u_{0} + v_{r} \log \frac{m_{0}}{m} \\ V = 0 + 10^{3} \times 2 .303 \log (\frac{m_{0}}{m_{0} / 100}) \\ = 10^{3} \times 2 .303 \log (100) \\ = 10^{3} \times 2 .303 \log (10^{2}) \\ = 10^{3} \times 2 .303 (2) = 10^{3} \times 4 .606 \\ V = 4 .6 km / s \end{array}$

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