A) 19.6 \[m{{s}^{-2}}\]
B) 30.2 \[m{{s}^{-2}}\]
C) 40 \[m{{s}^{-2}}\]
D) 49.8 \[m{{s}^{-2}}\]
Correct Answer: C
Solution :
Thrust force on the rocket \[{{F}_{t}}={{v}_{r}}=\left( -\frac{dm}{dt} \right)\] or \[ma={{v}_{r}}\left( -\frac{dm}{dt} \right)\] where \[{{v}_{r}}\] is the exhaust velocity of gases and \[-\frac{dm}{dt}\] is the mass of the ejected per unit time. Given, \[v=2400\,\,m{{s}^{-1}},-\frac{dm}{dt}=\frac{1}{60}\,kg/s\], \[m=1\,\,gk\] Substituting the values in above relation \[1\times a=2400\times \frac{1}{60}\] or \[a=40\,\,m{{s}^{-2}}\]
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