(D) The thrust force exerted on the rocket is given by $F_{\text{thrust}} = \left(\frac{dm}{dt}\right) V_{\text{rel}}$.The net force acting on the roc

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(D) The thrust force exerted on the rocket is given by $F_{\text{thrust}} = \left(\frac{dm}{dt}\right) V_{\text{rel}}$.The net force acting on the rocket is $F_{\text{net}} = F_{\text{thrust}} - mg = ma$.Substituting the given values: $m = 1000 \, \text{kg}$,$a = 20 \, \text{m s}^{-2}$,$V_{\text{rel}} = 500 \, \text{m s}^{-1}$,and $g = 10 \, \text{m s}^{-2}$.$\left(\frac{dm}{dt}\right) \times 500 - (1000 \times 10) = 1000 \times 20$$\left(\frac{dm}{dt}\right) \times 500 - 10000 = 20000$$\left(\frac{dm}{dt}\right) \times 500 = 30000$$\frac{dm}{dt} = \frac{30000}{500} = 60 \, \text{kg s}^{-1}$.

Class 11 Physics Newton's Laws of Motion and Friction Variable Mass System and Rocket Problem

Medium

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

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$600$
B
$500$
C
$10$
D
$60$

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Class 11

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Newton's Laws of Motion and Friction

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Variable Mass System and Rocket Problem

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$A$ solid disc of mass $M$ is held horizontally in the air by throwing $40$ stones per second vertically upwards to strike the disc,each with a velocity of $6\,m/s$. If the mass of each stone is $0.05\,kg$,what is the mass of the disc in $kg$? (Take $g = 10\,m/s^2$)

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