**Marks: 80**

**[Time : 3 hours]**

**Section A and B**

**INSTRUCTIONS TO CANDIDATES
**(1) All questions carry marks as indicated.

(2)Answer THREE questions from Section A and THREE questions from Section B.

(3)Due credit will be given to neatness and adequate dimensions.

(4) Assume suitable data wherever necessary.

(5) Illustrate your answers wherever necessary with the help of neat sketches.

(6) Use pen of Blue/Black ink/refill only for writing the answer book.

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**SECTION—A**

**1.** (a) Define couple and state its characteristics**. [03M]**

(b) State different system of forces. **[03M]**

(c) Replace the system of forces as shown in Fig. 1 into a single equivalent force and couple about point ‘A’. Forces are acting on L-bent as shown in fig. **[08M]**

**OR**

**2.** (a) State analytical and graphical conditions of equilibrium. **[04M]**

(b) Analyse the compound beam loaded as shown in Fig. 2. **[10M]**

**3.** (a) State assumptions made in the analysis of the trusses. **[04M]
**

(b) Analyse the truss loaded as shown in Fig. 3. Tabulate the results.

**OR**

**4.** (a) State laws of dry friction.** [04M]**

(b) Find the least value of ‘P ‘ that will just start the system of blocks moving to the right. Take μ=0.3. Assume pulley to be smooth. Refer Fig. 4. **[09M]**

**5.** (a) Locate the position of the centroid for semicircular plane lamina having radius `e using first principle. **[04M]
**

(b) Determine the principal moment of inertia and locate principal axes for the section as shown in Fig. 5.** [09M]**

**OR**

**6**. (a) State principle of virtual work. **[02M] **

(b) Analyse the beam loaded as shown in fig. 6 by using the virtual work principle.** [11M]**

**SECTION – B**

**7.** (a) The rectilinear motion of a particle is defined by a=\sqrt{v} . At the instant t=2 seconds, v=100 m/s and s = 100 m. Determine displacement of particle at t = 4 seconds. **[07M]**

(b) A projectile Is •• 240 m/s at a target ‘B’ located 600 in above the gun ‘A’ and at a horizontal distance of 3600 m. Determine the value of firing angle ‘α’. **[07M]**

**OR**

**8.** (a) The motion of a particle is given by a-t curve as shown in Fig. 7. Determine velocity and displacement after 8 sec and 12 sec interval using motion curves. [07 M]

(b) The rotation of flywheel is governed by equation ω=6t – 2 t^{1.5 }where (ω) is the angular velocity in rad/sec and ‘t’ is time in seconds. If the flywheel starts from rest, calculate its maximum angular velocity and displacement at that instant.

**[07M]**

**9.** a) State and explain D’Alembert’s principle. **[04M]**

(b) Two weights 800 N and 200 N are connected by a thread and move along a rough horizontal plane under the action of 400 N applied to 800 N weight as shown in Fig. 8. The coefficient of friction between sliding surface of weights and the plane is 0.3. Using D’Alembert’s principle acceleration of the blocks and tension in the thread. **[09M]**

**OR**

**10**. Two blocks A and B are released from rest on a 30° incline when they are 18 m apart. The coefficient of friction under the upper block A is 0.2 and that under Block B is 0.4. At what time block A reaches block B? The weights of blocks A and B are 100 N and 80 N respectively. Refer Fig. 9. **[13M]**

**11.** (a) Derive work-energy equation. **[05M]**

(b) A body weighing 300 N is pushed upon an inclined plane 30° with the horizontal. A 400 N force is acting parallel to the plane. If the initial velocity of the body is 1.5 m/s and the coefficient of friction is 0.2. Determine what velocity the body will have after moving 6 m. Refer Fig. 10. **[08M]**

**OR**

**12.** (a) Derive Linear-Impulse momentum equation **[04M]**

(b)Define coefficient of restitution. **[02M]
**

(c) A 400 N body moving to the right with a velocity of 8 m/s strikes a 250 N body moving to the left with a velocity of 12 m/sec on a straight line impinges centrally. Find the velocity of bodies after impact if the coefficient of restitution is 0.8. **[07M]**

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