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State and Explain principle of Transmissibility of a force A fine light string ABCDE whose extremity A is fixed, has weights W and W1 attached to it at B and C. It passes round a small smooth peg at D carrying a weight of 400 N at the free end E as shown in Fig. If in the position of equilibrium, BC is horizontal and AB and CD makes 150o and 120o with BC, find (i) the tensions in the portions AB, BC, CD and DE of the string, and (ii) magnitudes of W and W1. [8+8]

2. a) b)

Define friction. Explain the types of friction with examples. A block weighing 150 N is placed on a rough inclined plane whose slope is 3 vertical to 4 horizontal. A force of 50 N is applied on the body up the plane and parallel to it. Determine whether the block will be in equilibrium and find the value of the frictional force developed. [8+8]

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Classify and Explain the types of belt drives 5 Initial tension in a belt embracing th of the circumference is 1000 N. The coefficient 12 of friction between the belt and the pulley is 0.25. Determine the tension on tight and slack side and power transmitted if the speed of the belt is 120m/sec. [8+8]

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4. a)

Differentiate between centroid and centre of Gravity

b) 5.a)

[8+8]

Determine the moment of inertia about a diameter for a hollow sphere of mass m with inner and outer radii Ri and Ro respectively. Determine the moment of inertia of T-section as shown in Fig. 10.16 × 10.16 × 1.27 cm about an axis passing through the centre of the section and perpendicular to the stem or vertical leg. [8+8]

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Determine centroid of quadrant of a circle or quarter circle

A particle is travering a curved path of radius of curvature 400 m with the speed of 126 kmph and tangential acceleration of 5 m/sec2. Find the total acceleration of particle.[16]

7. a) b)

Explain simple Harmonic motion and give mathematical expression of it. A pulley whose axis passes through the centre O, carries loads as shown in Fig. Neglecting the inertia of the pulley and assuming that the cord is inextensible, determine the acceleration of the block A. How much weight should be added to or taken away from the block A, if the acceleration of the block A is required to be g/3 downwards. [8+8]

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8.

A body performing simple harmonic motion has a velocity =12 m/s when the

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displacement is 50 mm and 3 m/s when the displacement is 100mm, the displacement being measured from the midpoint.Calculate the frequency and amplitude of the motion. What is the acceleration when the displacement is 75mm. [16] ****

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Define result of a system of forces. What are the various methods to determine the resultant of concurrent forces b) A light chain PQRS is suspended from points P and S and two weights, 10 N at Q and W N at R cause it to hang as shown in Fig. Find W and tensions in different parts of the chain. [8+8]

Define limiting Friction and Coefficient of Static Friction. An effort of 150 N is required to just move a certain body up an inclined plane of angle 120, with force acting parallel to the plane. If the angle of inclination of the plane is changed to 150, the effort required was found to be 172 N when applied parallel to the plane. Find the weight of the body and the coefficient of friction. [8+8]

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Define (i) Slip of the belt (ii) Open belt drive and (iii) Cross belt drive. Find the power transmitted by a belt running over a pulley of 80 cm diameter at 150 rpm. Assume the coefficient of friction as 0.25. Angle of lap is 160o and tension on tight side is 200 N. [8+8]

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4. a) b)

State and Explain pappus theorem. Determine centroid of a Triangle.

5.a)

Show that the moment of inertia about a centroidal axis parallel to a side form a cube of mass m is I=1/2 ma2, where a is the length of a side.

[8+8]

Determine the moment of inertia of the z-section shown in Fig. about xx and yy axes, where xx and yy are the axes passing through the centroid of the figure. [8+8]

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The motion of a particle is expressed by the equations x = 4t + 2t2 and y 2 = 2t + 1.5 t , where x and y are in metres and t is in seconds. Find out the path, the velocity and the acceleration of the particle after 10 seconds from the start. [16]

7. a) b)

Explain what do you mean by Mechanical Vibrations and Free Vibrations. Two masses, 80 kg and 20 kg are connected by a thread and move along a rough horizontal plane under the action of a force 40 N applied to the first weight of 80 kg as shown in Fig. Determine the acceleration of the weights and the tension in the thread using D’ Alembert’s Principle. [8+8]

8.

The pendulum of Izod impact machine weights 35N. Its c.g is 1 metre from the axis of suspension and the striking knife is 15 cm below the c.g. The time for 20 small free oscillations is 43.5 seconds. In making a test, the pendulum is released from an angle of 60o to the vertical. Determine the striking velocity and the position of centre of percussion relative to the striking knife. [16]

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Differentiate static Friction and Kinetic Friction. A man wishing to slide a stone block of weight 100 N over a horizontal concrete floor, ties a rope to the block and pulls it in a direction inclined upward at an angle of 20o to the horizontal. Calculate the minimum pull necessary to slide the block if the coefficient of friction μ = 0.6. Calculate also the pull required if the inclination of the rope with the horizontal is equal to the angle of friction and prove that this is the least force required to slide the block. [8+8]

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1. a) Distinguish between moment about a point and moment about an axis. b) The frictionless pulley A shown if Fig. is supported by two bars AB and AC which are hinged at B and C to a vertical wall. The flexible cable DG hinged at D, goes over the pulley and supports a load of 20 kN at G. The angles between the various members are shown in the figure. Determine the forces in the bars AB and AC. Neglect the size of the pulley. [8+8]

3. a) b)

Distinguish between initial tension and centrifugal tension in a belt. Find the width of the belt required to transmit 1200 W to a pulley of diameter 30 cm, if the pulley rotates at 1500 rpm and the coefficient of friction between the belt and pulley is 0.2. Assume the angles of contact as 210o. The maximum tension in the belt is not to exceed 12 N/mm width of the belt. [8+8]

4. a) b)

How can you use to find centroid of a line or an area Determine centroid of a semi circle

5.a)

Determine the moment of inertia of a steel pipe with 90 mm outside diameter and 72.5 mm inside diameter and 3 m long with respect to its longitudinal axis. The density of steel is 7830 kg/m3. A built-in beam section is shown in Fig. Two equal channels are symmetrically about YY. Calculate the moment of inertia of the section about an XX-axis passing through the centroid. [8+8]

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[8+8]

A stone is thrown vertically up from the top of tower with a certain initial velocity. It reaches ground in 5-64 seconds. A second stone thrown down from the top of the same tower with the same initial velocity reaches ground in 3-6 seconds, Determine (i) height of tower and (ii) the initial velocity of the stones. [16]

7. a) b)

State and Explain Impulse momentum Equation. A body of mass 100 kg, moving with a velocity of 6 m/sec. collides directly with a stationary body of mass 50 kg. If the two bodies move together after impact, what is the common velocity. [8+8]

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A body moving with simple harmonic motion has an amplitude of 100 cm and a period of oscillation of 1 sec. What will be its velocity and acceleration 0.15 sec after passing an extreme position. [16]

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1. a) Distinguish between moment of force and moment of a couple b) A cord supported at A and B carries a load of 10 KN at D and a load of W at C a shown in Fig. Find the value of W so that CD remains horizontal. [8+8]

2. a) b)

Define (i) Efficiency of a screw jack (ii) Dynamic Friction. A uniform ladder of length 22 metres long rests against a vertical wall at an angle of 45o. The coefficient of friction between the ladder and the wall and ground are 0.33 and 0.5 respectively. If a man whose weight is one-half that of the ladder ascends the ladder, how high will he go up when the ladder starts slipping. [8+8]

3. a)

Explain the conditions for the maximum power transmitted by a belt from one pulley to another. A belt 8 mm thick and 150 mm width drives a pulley of 1.2 m diameter at 210 rpm. o 3 The angle of lap is 190 and mass of the belt material is 1 t/m . If the stress in the belt is not to exceed 1.5 N/mm2 and the coefficient of friction between belt and pulley is 0.3, determine the power transmitted when the centrifugal tension is (i) considered (ii) neglected. [8+8]

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If an area has two axes of symmetry then where does the centroid lie. Explain in detail Determine centre of gravity of a Right solid cone having radius of base r and height of cone h. [8+8]

5.a)

Find the moment of inertia of a brass cylindrical shaft 75 mm in diameter and 3 m long with respect to its geometric axis of rotation. Use a density of 8500 kg/m3.

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A cast iron channel section is shown in Fig. Calculate y and IXX. [8+8]

6.

A lift, starting from rest and going upwards, travels first 1800m with uniform acceleration and next 600m with uniform retardation before coming to rest again. If the rate of retardation is three times the rate of acceleration and total time of travel is 60 seconds, calculate the rate of acceleration, rate of retardation and maximum velocity.[16]

7. a)

Distinguish between (i) free vibration and forced vibration (ii) undamped and damped vibration. Three perfectly elastic balls A, B and C of masses 2 kg, 4 kg and 8 kg move along a line with velocities 4 m/sec, 1 m/sec and 0.75 m/sec. respectively. If ball A strikes ball B which in turn strikes ball C, determine the velocities of the three balls after impact. [8+8] The piston of a reciprocating pump has a motion which is simple harmonic in character. The stroke is 22.5 cm and it makes 200 complete oscillations in a minute. If it weights 4.54 N, Find: i) The accelerating force upon it in N and its velocity in m/sec when it is at a point 7.5 cm from mid-stroke position. ii) The maximum accelerating force. iii) The maximum velocity [6+5+5]

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