$A$ mass '$M$' is suspended by a rope from a rigid support at point '$P$' as shown in the figure. Another rope is tied at end '$Q$' and pulled horizontally with a force '$F$'. If the rope makes an angle '$\theta$' with the vertical,then the tension in the string '$PQ$' is

  • A
    $F \sin \theta$
  • B
    $\frac{F}{\sin \theta}$
  • C
    $F \cos \theta$
  • D
    $\frac{F}{\cos \theta}$

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$A$ body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ respectively. If $T_1 = \sqrt{3} T_2$,then the angles $\theta_1$ and $\theta_2$ are:

$A$ uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$. The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge?

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$P, Q$ and $R$ are three coplanar forces acting at a point and are in equilibrium. Given $P = 1.9318 \, kg \, wt$,$\sin {\theta _1} = 0.9659$,the value of $R$ is (in $kg \, wt$):

Statement-$I$: If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\vec{F}_{1} + \vec{F}_{2} = -\vec{F}_{3}$,then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement-$II$: $A$ triangle made up of three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ as its sides taken in the same order,satisfy the condition for translatory equilibrium.
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$A$ book of mass $5 \,kg$ is placed on a table and it is pressed by $10 \,N$ force. Then,the normal force exerted by the table on the book is ......... $N$.

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