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Laws of Motion Part 1

Section: Physics

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Question : 40 of 100

Marks: +1, -0

The initial mass of a rocket is

1000\,\text{kg}

. Calculate at what rate the fuel should be burnt, so that the rocket is given an acceleration of

20\,\text{ms}^{-1}

. The gases come out at a relative speed of

500\,\text{ms}^{-1}

with respect to the rocket [Use,

g=10\,\text{m/s}^{2}

[26 Aug 2021 Shift 1]

$6.0\times10^{2}\,\text{kg}\,\text{s}^{-1}$
$500\,\text{kg}\,\text{s}^{-1}$
$10\,\text{kg}\,\text{s}^{-1}$
$60\,\text{kg}\,\text{s}^{-1}$

Solution:

Given,

M=1000\,\text{kg},\ a=20\,\text{m/s}^{2}

v_{\text{relative}}=500\,\text{m/s},\ g=10\,\text{m/s}^{2}

The given situation is shown below

F_{\text{thrust}}=\frac{d}{dt}(M v_{\text{relative}})

\Rightarrow F_{\text{thrust}}=v_{\text{relative}}\left(\frac{dM}{dt}\right)

By Newton’s second law of motion,

\Rightarrow F_{\text{thrust}}-Mg=Ma

\Rightarrow v_{\text{relative}}\left(\frac{dM}{dt}\right)-Mg=Ma

\Rightarrow 500\left(\frac{dM}{dt}\right)-1000\times10=1000\times20

\Rightarrow 500\left(\frac{dM}{dt}\right)=1000(20+10)

\Rightarrow 500\left(\frac{dM}{dt}\right)=1000\times30

\Rightarrow \frac{dM}{dt}=\frac{1000\times30}{500}=60

\Rightarrow \frac{dM}{dt}=60\,\text{kg/s}

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