(D) Let the tension in the rope be $T$ and the angle the rope makes with the horizontal be $\theta$. For the weight $m = 15\, kg$ to be in equilibrium

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(D) Let the tension in the rope be $T$ and the angle the rope makes with the horizontal be $\theta$. For the weight $m = 15\, kg$ to be in equilibrium at the midpoint,the vertical components of the tension must balance the weight: $2T \sin \theta = mg$ Solving for tension $T$: $T = \frac{mg}{2 \sin \theta}$ To straighten the rope completely,the rope must be horizontal,which means the angle $\theta$ must be $0^\circ$. As $\theta \to 0^\circ$,$\sin \theta \to 0$. Therefore,$T = \frac{mg}{2 \times 0} = \infty$. Thus,an infinitely large tension is required to make the rope perfectly horizontal.

Class 11 Physics Newton's Laws of Motion and Friction The Common Forces and Equilibrium of Concurrent Forces

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Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. $A$ $15\, kg$ weight is attached to the rope at the mid-point,which now no longer remains horizontal. The minimum tension required to completely straighten the rope is

A
$15\, kg$
B
$7.5\, kg$
C
$5\, kg$
D
infinitely large

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Newton's Laws of Motion and Friction

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The Common Forces and Equilibrium of Concurrent Forces

$A$ mass $M$ is suspended by a rope from a rigid support at $A$ as shown in the figure. Another rope is tied at point $B$,and it is pulled horizontally with a force $F$. If the string $AB$ makes an angle $\theta$ with the vertical in equilibrium,then the tension in the string $AB$ is:

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$A$ small sphere is hung by a string fixed to a wall as shown in the figure. The sphere is pushed from the wall by a stick. The forces acting on the sphere are as shown. Then,identify the incorrect expression.

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Block $A$ of mass $4 \; kg$ is to be kept at rest against a smooth vertical wall by applying a force $F$ as shown in the figure. The force required is .......... $N$ $\left(g = 10 \; m/s^2\right)$. (in $\sqrt{2}$)

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Consider the following statements about the blocks shown in the diagram that are being pushed by a constant force $F$ on a frictionless table:
$A.$ All blocks move with the same acceleration.
$B.$ The net force on each block is the same.
Which of these statements is/are correct?

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$A$ body of mass $2 \ kg$ is suspended as shown in the figure. The tension $T_1$ (in $kg-wt$) in the horizontal string is :-

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Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. $A$ $15\, kg$ weight is attached to the rope at the mid-point,which now no longer remains horizontal. The minimum tension required to completely straighten the rope is

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$A$ mass $M$ is suspended by a rope from a rigid support at $A$ as shown in the figure. Another rope is tied at point $B$,and it is pulled horizontally with a force $F$. If the string $AB$ makes an angle $\theta$ with the vertical in equilibrium,then the tension in the string $AB$ is:

$A$ small sphere is hung by a string fixed to a wall as shown in the figure. The sphere is pushed from the wall by a stick. The forces acting on the sphere are as shown. Then,identify the incorrect expression.

Block $A$ of mass $4 \; kg$ is to be kept at rest against a smooth vertical wall by applying a force $F$ as shown in the figure. The force required is .......... $N$ $\left(g = 10 \; m/s^2\right)$. (in $\sqrt{2}$)

Consider the following statements about the blocks shown in the diagram that are being pushed by a constant force $F$ on a frictionless table:$A.$ All blocks move with the same acceleration.$B.$ The net force on each block is the same.Which of these statements is/are correct?

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Consider the following statements about the blocks shown in the diagram that are being pushed by a constant force $F$ on a frictionless table:
$A.$ All blocks move with the same acceleration.
$B.$ The net force on each block is the same.
Which of these statements is/are correct?