**Time-3 Hours
**

NB:

1. Question No. 1 is compulsory.

2. Attempt any three questions out of remaining five questions,

3. Assume suitable data if necessary stating them clearly.

4. Take g=9-81 m/s^{2} 5. Draw suitable sketches wherever necessary.

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**1. Attempt any four : **

(a) State and prove varignones theorem. **[05 M]**

(b) Find the resultant of the force system shown in fig. **[05 M]**

(c) Find the co-ordinate of the centroid of the area shown in fig. All dimensions are in cm. **[05 M]**

(d) A force of 500 N is acting on a black of 50Kg mass resting on a horizontal surface as shown in fig. Determine the velocity after the block has travelled a distance of 10m. Coeff. of kinetic friction = 0.5 **[05 M]**

(e) The position vector of a particle which moves in the X-Y plane is given by \overline{r} = (3t^{3}-4t^{2})i (0.5t^{4}) J m. Calculate velocity and acceleration at t=1 sec. **[05 M]**

(a) Find the resultant of the force acting on the bell crank level shown. Also locate its position write hinge B. **[08 M]**

(b) Determine the reaction at points of constant 1, 2 and 3. Assume smooth surfaces. **[05 M]**

(c) Two balls having 20Kg and 30Kg masses are moving towards each other with velocities of 10m/s and 5m/s respectively as shown in fig. If other impact the ball having 30kg mass is moving with 6m/s velocity to the right then determine the coefficient of restitution between the two balls. **[06 M]**

3. (a) Determine the centroid of the plant lamina shaded portion is removed. **[08 M]**

(b) Explain conditions for equilibrium for forces in spaces.

(c) A 30N block is released from rest. If slides down a rough incline having coefficient of friction 0.25. Determine the maximum compression of the spring. **[06 M]**

.

(a) Find the support reaction at A and B for the beam loaded as shown in fig. **[08 M]**

(b) The V-X graph of a rectilinear moving particle is shown. Find acceleration of the

particle at 20m, 80m and 200m. **[06 M]**

(c) A bar AB 2m long slides down the plane as shown. The end A slides on the horizontal floor with a velocity of 3 m/s . Determine the angular velocity of the rod AB and the velocity of end B for the position shown. **[06 M]**

**5.** a) Referring to the truss shown in fig. Find ** [08 M]**

I. Reaction at D and C

ii. Zero Force members

iii. Forces in members FE & DC by method of section.

iv. Forces in other members by method of joints.

(b) Determine the force 10 required to move the block A of 5000N weight up the inclined plane, coefficient of friction between all contact surfaces is 0.25. Neglect the weight of the wedge and the wedge angle is 15 degrees. **[06 M]**

(c) Determine the tension in a cable BC shown in fig by virtual work method. ** [06 M]**

**6.** (a) A 500N Crate kept on the top of a 150 sloping surface is pushed down the plane with an initial velocity of 20 m/s. If μs=0-5 and μk=04, Determine the distance travelled by the block and the time it will take as it comes to rest. ** [05 M]**

(b) Derive the equation of the path of a projectile and hence show that the path traced by a projectile is a parabolic curve. ** [05 M]**

c) A particle is moving in X-Y plane and its position is defined by \overline{r}=\left ( \frac{3}{2} t^{2}\right )i + \left ( \frac{2}{3} t^{3}\right ) J Find ratio of curvature when t= 2 sec. ** [05 M]**

(d) A force of 100N acts at a point P(-2,3, 5) m has its line of action passing through Q (10,3,4) m. Calculate moment of this force about origin (0,0,0). ** [05 M]**

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