Two equal heavy spheres,each of radius $r$,are in equilibrium within a smooth cup of radius $3r$. The ratio of the reaction between the cup and one sphere to that between the two spheres is:

For a particle to be in equilibrium,what must be the net force acting on it?

$A$ $50 \, kg$ homogeneous smooth sphere rests on a $30^{\circ}$ incline $A$ and bears against a smooth vertical wall $B$. Calculate the contact force at $A$. (Take $g = 10 \, m/s^2$)

$A$ 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 ......... $N$.

$A$ particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (assuming the particle is initially at rest):
$\vec{F}_1 = 5\hat{i} - 5\hat{j} + 5\hat{k}$
$\vec{F}_2 = 2\hat{i} + 8\hat{j} + 6\hat{k}$
$\vec{F}_3 = -6\hat{i} + 4\hat{j} - 7\hat{k}$
$\vec{F}_4 = -\hat{i} - 3\hat{j} - 2\hat{k}$
Then the particle will move:

As shown in the figure,the tension in the horizontal cord is $30 \, N$. The weight $W$ and the tension in the string $OA$ in Newton are: