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, \[{{v}_{r}}=2400\,m{{s}^{-1}},-\frac{dm}{dt}=\frac{1}{60}kg/s,\] \[m=1\,kg\] Substituting the values in above relation \[1\times a=2400\times \frac{1}{60}\] or \[a=40\,m{{s}^{-2}}\]
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