Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. $A$ and $B$ are roller supports, and $C$ is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is

A block of 50 kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is 0.3 . Neglecting pulley friction, the minimum value of M required to start the upward motion of the block is $\_\_\_\_$ kg (rounded off to 1 decimal place).

A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of $P = 100$ kN and $Q = 50$ kN. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is _________ kN (rounded off to 1 decimal place).

A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?

Take the acceleration due to gravity to be 𝑔 = 9.8 m/s². Options have been rounded off to one decimal place.