The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel 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 ]

Question

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel 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) 6.0 × 102 kg s -1 (B) 500 kg s -1 (C) 10 kg s -1 (D) 60 kg s -1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/463630f631a5ae300d695e81fa395455-.png" /> F text thrust =(( dm / dt ) ⋅ V textrel) (( dm / dt ) V textrel- mg )= ma ⇒ (( dm / dt )) × 500-103 × 10=103 × 20 ( dm / dt )=(60 kg / s )

Q. The initial mass of a rocket is $1000 k g$ . Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20 m s^{- 2}$ . The gases come out at a relative speed of $500 m s^{- 1}$ with respect to the rocket :
[Use $g = 10 m / s^{2}$ ]

$6.0 \times 1 0^{2} k g s^{- 1}$

$500 k g s^{- 1}$

$10 k g s^{- 1}$

$60 k g s^{- 1}$

$F_{thrust} = (\frac{d m}{d t} \cdot V_{rel})$
$(\frac{d m}{d t} V_{rel} - m g) = ma$
$\Rightarrow (\frac{d m}{d t}) \times 500 - 1 0^{3} \times 10 = 1 0^{3} \times 20$
$\frac{d m}{d t} = (60 k g / s)$

Q. The initial mass of a rocket is 1000kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20ms−2. The gases come out at a relative speed of 500ms−1 with respect to the rocket : [Use g=10m/s2 ]

6.0×102kgs−1

500kgs−1

10kgs−1

60kgs−1