1. Two forces are acting at a point as shown in Figure 1. Determine the magnitude and direction of the resultant choosing the x and y axes as shown and resolving the forces P and Q along these axes.

<img src='./qimages/7539-1.jpg'>

2. A bar AB of length 2l and negligible weight rests on two roller supports C and D placed at a distance l apart. For the reactions at the supports to be equal, find the distance of the end A of the bar, from the support C.

<img src='./qimages/7539-2.jpg'>

3. Determine the axial forces in the bars of a plane truss located as shown in Figure 3 below.

<img src='./qimages/7539-3.jpg'>

4. Find the moment of inertia of a plate with a circular hole about its centroidal x-axis.

<img src='./qimages/7539-4.jpg'>

5. Two wedges lift a heavy block of 8 kN as shown in Figure 5. If the angle of wedges is 10° and the coefficient of friction is 0·3 for all surfaces of contact, find the value of P required to drive the wedges under the load.

<img src='./qimages/7539-5.jpg'>

6. A boy throws a ball so that it may just clear a wall 4 m high. The boy is at a distance of 4·8 m from the wall. The ball was found to hit the ground at a distance of 4 m on the other side of the wall. Find the least velocity with which the ball can be thrown.

<img src='./qimages/7539-6.jpg'>

7. Calculate the pull in the cable during upward movement and pressure transmitted by a person of mass 65 kg to the floor during stopping, when the elevator mass is 600 kg and it starts from. the position of rest and moves upwards at a constant acceleration. It gains a velocity of 2·5 m/sec in a travel distance of 4 m. While stopping in a uniform retardation it stops in 2 seconds from a velocity of 2·5 m/sec. Assume g =10 m/sec^2.