For a free body diagram shown in the figure, the four forces are applied in the ' $x$ ' and ' $y$ ' directions. What additional force must be applied and at what angle with positive $x$-axis so that the net acceleration of body is zero?
$\sqrt{2} N , 45^{\circ}$
$\sqrt{2} N , 135^{\circ}$
$\frac{2}{\sqrt{3}} N , 30^{\circ}$
$2 N , 45^{\circ}$
Ten one-rupee coins are put on top of each other on a table. Each coin has a mass $m$ Give the magnitude and direction of
$(a)$ the force on the $7^{\text {th }}$ coin (counted from the bottom) due to all the coins on its top.
$(b)$ the force on the $7^{\text {th }}$ coin by the elghth coin,
$(c)$ the reaction of the $6^{\text {th }}$ coin on the $7^{\text {th }}$ coin.
The ends of a rope are held by two men who pulls on it with equal and opposite forces of magnitude $F$ each. Then the tension in the rope is
Two blocks of mass $2 \,kg$ and $4 kg$ are accelerated with same acceleration by a force $10 \,N$ as shown in figure on a smooth horizontal surface. Then the spring force between the two blocks will be .......... $N$ (spring is massless)
A false balance has equal arms. An object weigh $X$ when placed in one pan and $Y$ when placed in other pan, then the weight $W$ of the object is equal to