JEE Main & Advanced Physics NLM, Friction, Circular Motion Question Bank Topic Test - Newton's Laws Of Motion

A rocket of initial mass 6000 kg ejects mass at a constant rate of 20 kg/s with constant relative speed of 10 km/s. What is the acceleration of the rocket after 50 second, (Neglect gravity)

A) \[50\,m/{{s}^{2}}\]

B) \[40\,m/{{s}^{2}}\]

C) \[60\,m/{{s}^{2}}\]

D) 30 m/\[\Omega \]

Correct Answer: B

Solution :

[b] Mass of the rocket after 50 seconds is: \[m={{m}_{0}}-\mu t\]

Here \[\mu =20\,kg/s\]\[=(6000)-(20)(50)=5000\,kg\]

Thrust force \[F={{V}_{rel\mu }}\]

\[\therefore \]\[F=(10\times {{10}^{3}}\,m/s)(20\,kg/s)\]\[=2.0\times {{10}^{5}}N\]

\[\therefore \] Acceleration \[a=F/m=\frac{2\times {{10}^{5}}}{5000}=40\,m/{{s}^{2}}\]