(C) The thrust force on the rocket is given by $F = v_{rel} \cdot \frac{dM}{dt}$.Given: $v_{rel} = 5 \ km/s = 5000 \ m/s$,$\frac{dM}{dt} = 10 \ kg/s$.

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(C) The thrust force on the rocket is given by $F = v_{rel} \cdot \frac{dM}{dt}$.Given: $v_{rel} = 5 \ km/s = 5000 \ m/s$,$\frac{dM}{dt} = 10 \ kg/s$.$F = 5000 \times 10 = 50000 \ N$.The mass of the rocket at time $t$ is $M(t) = M_0 - (\frac{dM}{dt})t$.At $t = 50 \ s$,$M(50) = 1500 - (10 \times 50) = 1500 - 500 = 1000 \ kg$.Using Newton's second law,$F = M(t) \cdot a$.$a = \frac{F}{M(t)} = \frac{50000}{1000} = 50 \ ms^{-2}$.

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

Medium

$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. The acceleration of the rocket $50 \ s$ after the blast,neglecting gravity,is $x \ ms^{-2}$. Find the value of $x$.

A
$10$
B
$25$
C
$50$
D
$100$

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Newton's Laws of Motion and Friction

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Variable Mass System and Rocket Problem

In a rocket,fuel burns at the rate of $2 \, kg/s$. This fuel is ejected from the rocket with a velocity of $80 \, km/s$. The force exerted on the rocket is ............. $N$.

Easy

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Gravels are dropped on a conveyor belt at the rate of $0.5 \, kg/s$. The extra force required in newtons to keep the belt moving at $2 \, m/s$ is

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If the force on a rocket having an exhaust velocity of $300 \, m/s$ is $210 \, N$,then the rate of combustion of the fuel is ........... $kg/s$.

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$A$ rocket of mass $1000 \, kg$ exhausts gases at a rate of $4 \, kg/s$ with a velocity of $3000 \, m/s$. The thrust developed on the rocket is ........ $N$.

Easy

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$A$ rocket with an initial mass $m_0$ is going up with a constant acceleration $a$ by exhausting gases with a velocity $v$ relative to the rocket motion. The mass of the rocket at any instant of time $t$ is (assume that no other forces act on it).

DifficultAP EAMCET 2018

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$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. The acceleration of the rocket $50 \ s$ after the blast,neglecting gravity,is $x \ ms^{-2}$. Find the value of $x$.

Similar Questions

In a rocket,fuel burns at the rate of $2 \, kg/s$. This fuel is ejected from the rocket with a velocity of $80 \, km/s$. The force exerted on the rocket is ............. $N$.

Gravels are dropped on a conveyor belt at the rate of $0.5 \, kg/s$. The extra force required in newtons to keep the belt moving at $2 \, m/s$ is

If the force on a rocket having an exhaust velocity of $300 \, m/s$ is $210 \, N$,then the rate of combustion of the fuel is ........... $kg/s$.

$A$ rocket of mass $1000 \, kg$ exhausts gases at a rate of $4 \, kg/s$ with a velocity of $3000 \, m/s$. The thrust developed on the rocket is ........ $N$.

$A$ rocket with an initial mass $m_0$ is going up with a constant acceleration $a$ by exhausting gases with a velocity $v$ relative to the rocket motion. The mass of the rocket at any instant of time $t$ is (assume that no other forces act on it).

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