JEE Mains · Physics · STD 11 - 4.1 newtons laws of motion
The initial mass of a rocket is \(1000\, {kg} .\) Calculate at what rate the fuel (In \({kg} {s}^{-1}\)) should be burnt so that the rocket is given an acceleration of \(20 \,{ms}^{-2}\). The gases come out at a relative speed of \(500\, {ms}^{-1}\) with respect to the rocket : [Use \( g = 10\, {m} / {s}^{2}\) ]
- A \(600\)
- B \(500\)
- C \(10\)
- D \(60\)
Answer & Solution
Correct Answer
(D) \(60\)
Step-by-step Solution
Detailed explanation
\(F_{\text {thrust }}=\left(\frac{{dm}}{{dt}} \cdot {V}_{{rel}}\right)\) \(\left(\frac{{dm}}{{dt}} {V}_{{rel}}-{mg}\right)={ma}\) \(\Rightarrow\left(\frac{{dm}}{{dt}}\right) \times 500-10^{3} \times 10=10^{3} \times 20\) \(\frac{{d} {m}}{{dt}}=(60 \,{kg} / {s})\)
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