(D) The acceleration of the center of mass of the system is given by $a_{cm} = \frac{ F_{ext} }{ M_{total} }$.Here,the external force is $F$ and the t

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(D) The acceleration of the center of mass of the system is given by $a_{cm} = \frac{ F_{ext} }{ M_{total} }$.Here,the external force is $F$ and the total mass is $M + M = 2M$.So,$a_{cm} = \frac{ F }{ 2M }$.Also,$a_{cm} = \frac{ m_A a_A + m_B a_B }{ m_A + m_B }$,where $a_A = a$ (acceleration of mass $A$) and $a_B$ is the acceleration of mass $B$.Substituting the values: $\frac{ F }{ 2M } = \frac{ M(a) + M(a_B) }{ 2M }$.Canceling $2M$ from both sides,we get $F = Ma + Ma_B$.Rearranging for $a_B$,we get $Ma_B = F - Ma$.Therefore,$a_B = \frac{ F - Ma }{ M }$.

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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Two masses $A$ and $B$,each of mass $M$,are connected by a massless spring. $A$ force $F$ acts on the mass $B$ as shown in the figure. If the mass $A$ starts moving away from mass $B$ with acceleration $a$,then the acceleration of mass $B$ will be:

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A
$\frac{ Ma - F }{ M }$
B
$\frac{ MF }{ F + Ma }$
C
$\frac{ F + Ma }{ M }$
D
$\frac{ F - Ma }{ M }$

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Class 11

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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)

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$A$ car of mass $1250 \ kg$ is moving at $30 \ m/s$. Its engine delivers $30 \ kW$ while the resistive force due to the surface is $750 \ N$. What is the maximum acceleration that can be given to the car in $m/s^2$?

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Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. Calculate $T_1$ and $T_2$ when the whole system is moving upwards with an acceleration $a = 2\, m/s^2$ (use $g = 9.8\, m/s^2$).

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Three blocks $A$,$B$,and $C$ of masses $5 \text{ kg}$,$3 \text{ kg}$,and $2 \text{ kg}$ respectively are pulled on a horizontal smooth surface by a force of $80 \text{ N}$ as shown in the figure. The tensions $T_1$ and $T_2$ in the strings are respectively:

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Two blocks of masses $5\, kg$ and $4\, kg$ are in contact with each other on a frictionless table. When a horizontal force of $9\, N$ is applied to the block of mass $5\, kg$,then the value of the force of contact between the two blocks is ........ $N$.

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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. ............ $N$

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Two masses $A$ and $B$,each of mass $M$,are connected by a massless spring. $A$ force $F$ acts on the mass $B$ as shown in the figure. If the mass $A$ starts moving away from mass $B$ with acceleration $a$,then the acceleration of mass $B$ will be:

Similar Questions

$A$ car of mass $1250 \ kg$ is moving at $30 \ m/s$. Its engine delivers $30 \ kW$ while the resistive force due to the surface is $750 \ N$. What is the maximum acceleration that can be given to the car in $m/s^2$?

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. Calculate $T_1$ and $T_2$ when the whole system is moving upwards with an acceleration $a = 2\, m/s^2$ (use $g = 9.8\, m/s^2$).

Three blocks $A$,$B$,and $C$ of masses $5 \text{ kg}$,$3 \text{ kg}$,and $2 \text{ kg}$ respectively are pulled on a horizontal smooth surface by a force of $80 \text{ N}$ as shown in the figure. The tensions $T_1$ and $T_2$ in the strings are respectively:

Two blocks of masses $5\, kg$ and $4\, kg$ are in contact with each other on a frictionless table. When a horizontal force of $9\, N$ is applied to the block of mass $5\, kg$,then the value of the force of contact between the two blocks is ........ $N$.

$A$ 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. ............ $N$

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