(B) Let $m_A = 250 \ kg$ be the mass of the platform plus the boy,and $m_B = 500 \ kg$ be the mass of the box.The force applied by the boy on the rope

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(B) Let $m_A = 250 \ kg$ be the mass of the platform plus the boy,and $m_B = 500 \ kg$ be the mass of the box.The force applied by the boy on the rope is $F = 50 \ N$. By Newton's third law,the tension in the rope is $T = 50 \ N$.For platform $A$,the force $T$ acts towards the right: $a_A = \frac{T}{m_A} = \frac{50}{250} = 0.2 \ m/s^2$.For box $B$,the force $T$ acts towards the left: $a_B = \frac{T}{m_B} = \frac{50}{500} = 0.1 \ m/s^2$.Since they move in opposite directions,the relative acceleration is $a_{rel} = a_A - (-a_B) = 0.2 + 0.1 = 0.3 \ m/s^2$.After $t = 5 \ s$,the relative velocity is $v_{rel} = a_{rel} \times t = 0.3 \times 5 = 1.5 \ m/s$.

Class 11 Physics Newton's Laws of Motion and Friction Motion of Body (or Connected Bodies in horizontal or vertical) (by String or Contact)

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The figure shows a boy on a horizontal platform $A$ on a smooth horizontal surface,holding a rope attached to a box $B$. The boy pulls the rope with a constant force of $50 \ N$. (The boy does not slip over the platform). The combined mass of platform $A$ and the boy is $250 \ kg$,and that of box $B$ is $500 \ kg$. The velocity of $A$ relative to the box $B$,$5 \ s$ after the boy on $A$ begins to pull the rope,will be ............ $m/s$.

A
$1$
B
$1.5$
C
$2$
D
$0.5$

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Chapter

Newton's Laws of Motion and Friction

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Motion of Body (or Connected Bodies in horizontal or vertical) (by String or Contact)

$A$ block of mass $m$ is kept on a platform which starts from rest with constant acceleration $g/2$ upward,as shown in the figure. Work done by the normal reaction on the block in time $t$ is

MediumJEE MAIN 2019

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$A$ uniform rope of mass $1.0 \ kg$ is connected to a box of mass $2.0 \ kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6 \ N$. Find the tension at the midpoint of the rope. ............ $N$

Medium

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If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person,then the maximum acceleration with which the person can safely climb up the rope is ($g$ = acceleration due to gravity).

MediumAP EAMCET 2025

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If a ship of mass $4 \times 10^{7} \,kg$ initially at rest is pulled by a force of $5 \times 10^{4} \,N$ through a distance of $4 \,m$, then the speed of the ship will be (resistance due to water is negligible). (in $\,ms^{-1}$)

MediumMHT CET 2012

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$A$ body of mass $2 \, kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$. It starts from rest and was at the origin initially. After $4 \, s$,its new coordinates are $(8, b, 20)$. The value of $b$ is ........ . (Round off to the Nearest Integer)

MediumJEE MAIN 2021

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$A$ block of mass $m$ is kept on a platform which starts from rest with constant acceleration $g/2$ upward,as shown in the figure. Work done by the normal reaction on the block in time $t$ is

$A$ uniform rope of mass $1.0 \ kg$ is connected to a box of mass $2.0 \ kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6 \ N$. Find the tension at the midpoint of the rope. ............ $N$

If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person,then the maximum acceleration with which the person can safely climb up the rope is ($g$ = acceleration due to gravity).

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$A$ body of mass $2 \, kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$. It starts from rest and was at the origin initially. After $4 \, s$,its new coordinates are $(8, b, 20)$. The value of $b$ is ........ . (Round off to the Nearest Integer)

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