(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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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)

Three blocks of masses $m_1, m_2$ and $m_3$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $F = 40 \, N$. If $m_1 = 10 \, kg, m_2 = 6 \, kg$ and $m_3 = 4 \, kg$,the tension $T_2$ (between $m_1$ and $m_2$) will be ........ $N$.

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$A$ block of mass $M$ is kept on a platform which starts accelerating upwards from rest with a constant acceleration $a$. During the time interval $T$,the work done by the contact force on mass $M$ is

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$A$ trolley of mass $20 \ kg$ is attached to a block of mass $4 \ kg$ by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between the trolley and the surface is $0.02$,then the acceleration of the trolley and block system is (take $g=10 \ ms^{-2}$):- (in $ms^{-2}$)

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Two blocks of masses $6 \ kg$ and $4 \ kg$ are placed in contact with each other on a smooth surface as shown. If a force of $5 \ N$ is applied on the heavier block,the force on the lighter block is (in $N$)

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What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

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Three blocks of masses $m_1, m_2$ and $m_3$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $F = 40 \, N$. If $m_1 = 10 \, kg, m_2 = 6 \, kg$ and $m_3 = 4 \, kg$,the tension $T_2$ (between $m_1$ and $m_2$) will be ........ $N$.

$A$ block of mass $M$ is kept on a platform which starts accelerating upwards from rest with a constant acceleration $a$. During the time interval $T$,the work done by the contact force on mass $M$ is

Two blocks of masses $6 \ kg$ and $4 \ kg$ are placed in contact with each other on a smooth surface as shown. If a force of $5 \ N$ is applied on the heavier block,the force on the lighter block is (in $N$)

What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

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