Time: 3 hours Maximum Marks: 60

Note:- This paper consists of Three Sections. Section A is compulsory. Do any Four questions from Section B and any Two question from Section C

Section-A

Marks : 20

1. 1. (a) Differentiate between angle of friction and angle of repose.

(b) Sketch the equilibrium of a body of weight ‘w’ on an inclined plane subjected to a force P applied parallel to the plane.

(c ) State and explain the parallel axis theorem.

(d) Explain how you will find the velocity of a projectile after a given interval from the constant of projection.

(e) State and explain the triangle lay of forces.

(f) Explain, what is impulse, how do you find it?

(g) Sketch and analyse an oblique impact on a smooth fixed plane.

(h) Differentiate between Kinematics and Kinetics.

(i)State and explain the law of conservation of energy.

(j) Differentiate between free and forced vibrations and transient and steady state vibrations.

Section-B

Marks : 5 Each

2. A rope is fastened at the points (0,0) and (9,0) carries a 200 N weight and an unknown weight as shown in the fig.-1. The vertices of the rope polygon lie at the points (2,3) and (5,4). Determine the magnitudes of the forces in the three parts of the rope and the magnitude of the weight W.

3. A block weighing 800 N rests on an inclined plane 4 : 3 (4 horizontal to 3 vertical0. The coefficient of friction is 0.4. Determine the value of the force appied parallel to the plane to cause motion to impend:

(a) (a) up the plane

(b) (b) down the plane

3. Determine the coordinates of the area shown shaded in fig.-2.

5. A stone is thrown horizontally with a velocity 2gh from the top of a tower of height h. Find, where and with what velocity will it strike the level ground through the foot of the tower.

6. A cylinder oscillates about a fixed axis with a frequency of 10 cycles per minute. If the motion is harmonic with an amplitude of 0.10 rad, find the maximum acceleration in rad/s².

Section-C

Marks : 10 Each

7. 7. A particle moves in a straight line. Its movement is represented by the equation: S=12t+2t²-t³ where, S is in metres and t, in seconds.

Determine:

(a) displacement, velocity and acceleration 2 seconds after start;

(b) displacement and acceleration when velocity is zero, and

(c ) displacement and velocity when acceleration is zero.

8. A pile hammer weighing 8 kn falls freely from a height of 2.0 m on a pile weighing 4 kN. For each blow, the pile is driven by 100 mm. Determine :

(a) (a) resistance of the ground

(b) (b) loss of Kinetic Energy during the impact, and

Draw free body diagram for the arrangement og two 1.0 kN , 300 mm radius cylinderical rollers, shown in Fig.-3. Also determine the magnitudes of all the forces. Assume all surfaces are frictionless.

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