See Figure given below. A mass of 6 kg is suspended by a rope of length 2 m from ceiling. A fo

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4-1.Newton's Laws of Motion

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See Figure given below. A mass of $6 \;kg$ is suspended by a rope of length $2 \;m$ from the ceiling. A force of $50\; N$ in the horizontal direction is applied at the midpoint $P$ of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ? (Take $g = 10 \;m s^{-2}$). Neglect the mass of the rope.

$30$

$40$

$75$

$60$

Solution

Consider the equilibrium of the weight $W$

$\text { Clearly, } T_{2}=6 \times 10=60 \,N$

Consider the equilibrium of the point P under the action of three forces – the tensions $T_{1}$ and $T_{2},$ and the horizontal force $50 N$. The horizontal and vertical components of the resultant force must vanish separately

$T_{1} \cos \theta=T_{2}=60 \,N$

$T_{1} \sin \theta=50 \,N$which gives that

$\tan \theta=\frac{5}{6} \text { or } \theta=\tan ^{-1}\left(\frac{5}{6}\right)=40^{\circ}$

Standard 11

Physics

A piece of wire is bent in the shape of a parabola $y=k x^2$ ( $y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $\alpha$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is

hard

(IIT-2009)

Explain primary concept of force.

easy

Which of the following groups of forces could be in equibrium

easy

There are four forces acting at a point $P$ produced by strings as shown in figure, point $P$ is at rest. The forces $F_1$ and $F_2$ are respectively:-