(D) Let the acceleration of the system be $a$. Since the blocks are connected by a spring and move together on a smooth horizontal surface,both blocks

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(D) Let the acceleration of the system be $a$. Since the blocks are connected by a spring and move together on a smooth horizontal surface,both blocks will have the same acceleration $a$.For the system of two blocks,the net force is $F$. According to Newton's second law,$F = (m + M)a$,which gives $a = \frac{F}{m + M}$.The force acting on the block of mass $m$ is the spring force $T$. Applying Newton's second law to the block of mass $m$,we get $T = ma$.Substituting the value of $a$,we get $T = m \left( \frac{F}{m + M} \right) = \frac{mF}{m + M}$.

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

Medium

$A$ block of mass $m$ is connected to another block of mass $M$ by a massless spring of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially,the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force acting on the block of mass $m$.

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A
$\frac{MF}{m + M}$
B
$\frac{mF}{M}$
C
$\frac{(m + M)F}{m}$
D
$\frac{mF}{m + M}$

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Class 11

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Chapter

Newton's Laws of Motion and Friction

Subtopic

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

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

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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 in $N$.

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Two blocks are in contact on a frictionless table. One has mass $m$ and the other $2\,m$. $A$ force $F$ is applied on $2\,m$ as shown in the figure. Now,the same force $F$ is applied from the right on $m$. In the two cases respectively,what is the ratio of the contact force between the two blocks?

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The figure shows four blocks that are being pulled along a smooth horizontal surface. The masses of the blocks and the tension in one string are given. The pulling force $F$ is ............ $N$.

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The figure shows two blocks connected by a light inextensible string. $A$ force of $10 \,N$ is applied on the bigger block at $60^{\circ}$ with the horizontal. The tension in the string connecting the two masses is ....... $N$.

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

$A$ 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 in $N$.

Two blocks are in contact on a frictionless table. One has mass $m$ and the other $2\,m$. $A$ force $F$ is applied on $2\,m$ as shown in the figure. Now,the same force $F$ is applied from the right on $m$. In the two cases respectively,what is the ratio of the contact force between the two blocks?

The figure shows four blocks that are being pulled along a smooth horizontal surface. The masses of the blocks and the tension in one string are given. The pulling force $F$ is ............ $N$.

The figure shows two blocks connected by a light inextensible string. $A$ force of $10 \,N$ is applied on the bigger block at $60^{\circ}$ with the horizontal. The tension in the string connecting the two masses is ....... $N$.

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