1) Petrol engine has stroke of 120mm and connecting rod is 3 times the crank length. Crank rotates at 1500 r.p.m. in clockwise direction. Find out:

(a) Velocity and acceleration of the piston and

(b) Angular velocity and angular acceleration of connecting rod when piston has travelled one fourth of its stroke form Inner Dead Centre.

2) With neat and suitable sketches describe the condition of static equilibrium of member with

(a) two forces

(b) three forces

(c) two forces and a torque

(d) two couples

3) Four masses m₁, m₂, m₃ and m₄ are 200 kg, 300 kg, 240 kg and 260 kg respectively. Corresponding radii of rotation are 0.2 m, 0.15m, 0.25m and 0.3m respectively and angles between successive masses are 45^o, 75^o and 135^o. Determine the position and magnitude of balance mass needed, if its radius of rotation is 0.2 m.

4) Single cylinder reciprocating engine has speed of 240 r.p.m., stroke 300mm, mass of reciprocating parts 50 kg, mass of revolving parts at 150mm radius 37 kg. If two-third of reciprocating masses and all revolving parts are to be balanced, determine:

(a) Balance mass required at a radius o 400 mm and

(b) Residual unbalanced force when crank has rotated 60^o from Top Dead Centre.

5) A shaft 50mm diameter and 3meter long is simply supported at the ends and carries three loads of 1000 N, 1500 N and 750 n at 1m, 2m and 2.5m from the left support. The young’s modulus for shaft material is 200 GN/m². Find the frequency of transverse vibration.