(B) The force required to pull the rope is equal to the rate of change of momentum of the rope being set into motion.As the rope is pulled,a segment o

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(B) The force required to pull the rope is equal to the rate of change of momentum of the rope being set into motion.As the rope is pulled,a segment of the heap at rest is accelerated to speed $v$.The mass of the rope pulled in time $dt$ is $dm = \lambda dx$,where $dx = v dt$.Thus,$dm = \lambda v dt$.The force $F$ required is given by the thrust force formula: $F = v_{rel} \frac{dm}{dt}$.Here,$v_{rel} = v$ (the speed at which the rope is being pulled from rest).Substituting the values: $F = v \cdot \frac{\lambda v dt}{dt} = \lambda v^2$.

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

Medium

$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

A
$2\lambda v^2$
B
$\lambda v^2$
C
$\lambda lg$,where $l$ is the length that you have pulled straight
D
$\frac{\lambda v^2}{2}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

Subtopic

Variable Mass System and Rocket Problem

$A$ rocket moves straight upward with zero initial velocity and with an acceleration of $20 \,m/s^2$. It runs out of fuel and stops accelerating at the end of $5^{th} \,sec$. It reaches a maximum height and falls back to the earth. The speed when it hits the ground is (Take $g = 10 \,m/s^2$):

MediumTS EAMCET 2022

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$A$ $600\; kg$ rocket is set for a vertical firing. If the exhaust speed is $1000\; m/s$,the mass of the gas ejected per second (in $kg/s$) to supply the thrust needed to overcome the weight of the rocket is

MediumAIPMT 1990

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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.

EasyAIIMS 2001

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$A$ rifle of $20 \,kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} \,kg$ and its final velocity is $400 \,ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $\,N$)?

EasyTS EAMCET 2007

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$A$ balloon with mass $m$ is descending vertically with an acceleration $a$ (where $a < g$). The mass to be removed from the balloon so that it starts moving vertically up with an acceleration $a$ is:

MediumAP EAMCET 2025

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$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

Similar Questions

$A$ rocket moves straight upward with zero initial velocity and with an acceleration of $20 \,m/s^2$. It runs out of fuel and stops accelerating at the end of $5^{th} \,sec$. It reaches a maximum height and falls back to the earth. The speed when it hits the ground is (Take $g = 10 \,m/s^2$):

$A$ $600\; kg$ rocket is set for a vertical firing. If the exhaust speed is $1000\; m/s$,the mass of the gas ejected per second (in $kg/s$) to supply the thrust needed to overcome the weight of the rocket is

$Assertion$ : $A$ 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.

$A$ rifle of $20 \,kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} \,kg$ and its final velocity is $400 \,ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $\,N$)?

$A$ balloon with mass $m$ is descending vertically with an acceleration $a$ (where $a < g$). The mass to be removed from the balloon so that it starts moving vertically up with an acceleration $a$ is:

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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.