1. Choose the correct answer from the given alternatives.

If the resultant of two forces has the same magnitude as either of the forces, then the angle between the two forces is

30°

45°

60°

120°

The moment of inertia of a spherical shell of mass m and radius r about a diameter is

1/2 mr^2

2/3 mr^2

2/5 mr^2

3/5 mr^2

Power is defined as

Total work done

Capacity to do the work

Rate of doing the work

Rate of change of momentum

Force in U2 L2 member of the truss shown in

<img src='./qimages/13127-1d.jpg'>

P

P/2

P/4

Zero

Frictional resistance does not depend upon

Normal reaction

Coefficient of friction

Contact area

All of the above

The maximum displacement of a particle executing S.H.M. corresponds to

zero potential energy and maximum kinetic energy

zero kinetic energy and maximum potential energy

maximum kinetic energy and maximum potential energy

minimum kinetic energy and minimum potential energy

A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is

1/3

2/3

1/9

8/9

2. State the parallelogram law of forces.

A rod AB carries three loads of 30 90 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, determine the point at which the rod will balance.

3. A beam AB is hinged at A and is supported at C as shown in Figure 2. Find out the reaction at A and C.

<img src='./qimages/13127-3.jpg'>

4. A crate weighing 5 kN is kept on an inclined plane making an angle of 30° with the horizontal. Ref: Figure

Determine the P (the. horizontal force) required to move the crate up the plane.

What is the minimum value of P required to prevent the crate from sliding down the plane? Assume m =0·25.

<img src='./qimages/13127-4b.jpg'>

5. Determine the centroid of a plane with uniform mass per unit area having a shape given in Figure.

<img src='./qimages/13127-5.jpg'>

6. A pile of mass 1500 kg is driven 450 mm into the ground by a pile driver weighing 200 N falling from a height of 2.0 m. Find the average resistance of the ground to penetration of pile, assuming g =10 m/sec^2.

7. A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string What is the maximum speed with which the stone can be whirled around, if the string can withstand a maximum tension of 200