Uncategorized: Practice Problem & Solution

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

The thrust of a rocket is given by \(T = v_e \frac{dm}{dt}\,) where \(v_e\) is the exhaust speed and \(frac{dm}{dt}\) is the mass ejection rate. To overcome the rocket's weight \(Mg\), the thrust must equal the weight. So, \(v_e \frac{dm}{dt} = Mg\). Given \(M = 600 \text{ kg}\,) \(v_e = 1000 \text{ m/s}\,) and assuming \(g \approx 10 \text{ m/s}^2\), we have \(1000 \frac{dm}{dt} = 600 \times 10\). Thus, \(frac{dm}{dt} = 6 \text{ kg/s}\).