$A$ $50 \, kg$ 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 $g = 10 \, m/s^2$)

$A$ flexible chain of weight $W$ hangs between two fixed points $A$ and $B$ which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is $\theta$. What is the tension of the chain at the mid-point?

$A$ body is in equilibrium under the action of three coplanar forces $P, Q$ and $R$ as shown in the figure. Select the correct statement.

$A$ mass of $10\,kg$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point,the rope deviates at an angle of $45^o$ from the vertical. If the suspended mass is at equilibrium,the magnitude of the force applied is .......... $N$ $(g = 10\,ms^{-2})$.

The following forces start acting on a particle at rest at the origin of the coordinate system simultaneously: ${\vec F_1} = -4\hat i - 5\hat j + 5\hat k$,${\vec F_2} = 5\hat i + 8\hat j + 6\hat k$,${\vec F_3} = -3\hat i + 4\hat j - 7\hat k$,and ${\vec F_4} = 2\hat i - 3\hat j - 2\hat k$. The particle will move:

$A$ block is being pulled by a force $F$ on a long frictionless level floor. The magnitude of the force is gradually increased from zero until the block lifts off the floor. Immediately after the block leaves the floor,its acceleration is