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Physics · LAWS OF MOTION
हिन्दीA rocket has an initial mass \( m_0 = 1000\text{ kg} \). It burns fuel and ejects exhaust gas at a constant relative velocity \( u = 500\text{ m/s} \) at a rate of \( 10\text{ kg/s} \). Neglecting gravitational effects, the instantaneous acceleration of the rocket at time \( t = 50\text{ s} \) after launch is:
Correct answer · Option 2
10 m/s²
Explanation
Mass at \( t = 50\text{ s} \) is \( m(t) = 1000 - (10 \times 50) = 500\text{ kg} \). Thrust force \( F = u \frac{dm}{dt} = 500 \times 10 = 5000\text{ N} \). Acceleration \( a = \frac{F}{m(t)} = \frac{5000}{500} = 10\text{ m/s}^2 \).
