(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 $g = 10 \, \text{m s}^{-2}$]

JEE MAIN 2021 All JEE MAIN

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

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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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Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.

Medium

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$A$ trolley containing water has a total mass of $4000\, kg$ and is moving at a speed of $40\, m/s$. Water starts leaking from a hole at the bottom of the trolley at a rate of $8\, kg/s$. What is the speed of the trolley after $50\, s$?

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$A$ sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed $v$ of the belt,i.e.,$\frac{dm}{dt} \propto \sqrt{v}$. If $P$ is the power delivered to run the belt at constant speed,then which of the following relationships is true?

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$A$ rocket of mass $4000\, kg$ is set for vertical firing. How much gas must be ejected per second so that the rocket may have an initial upward acceleration of magnitude $19.6\, m/s^2$? [Exhaust speed of fuel $= 980\, m/s$.]

Medium

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$Assertion$ : $A$ rocket moves forward by pushing the surrounding air backwards.
$Reason$ : It derives the necessary thrust to move forward according to Newton's third law of motion.

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Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.

$A$ trolley containing water has a total mass of $4000\, kg$ and is moving at a speed of $40\, m/s$. Water starts leaking from a hole at the bottom of the trolley at a rate of $8\, kg/s$. What is the speed of the trolley after $50\, s$?

$A$ sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed $v$ of the belt,i.e.,$\frac{dm}{dt} \propto \sqrt{v}$. If $P$ is the power delivered to run the belt at constant speed,then which of the following relationships is true?

$A$ rocket of mass $4000\, kg$ is set for vertical firing. How much gas must be ejected per second so that the rocket may have an initial upward acceleration of magnitude $19.6\, m/s^2$? [Exhaust speed of fuel $= 980\, m/s$.]

$Assertion$ : $A$ rocket moves forward by pushing the surrounding air backwards.$Reason$ : It derives the necessary thrust to move forward according to Newton's third law of motion.

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$Assertion$ : $A$ rocket moves forward by pushing the surrounding air backwards.
$Reason$ : It derives the necessary thrust to move forward according to Newton's third law of motion.