Engineering Mechanics PYQs

A light string ABCDE whose extremity A is fixed, has weights $W_1$ and $W_2$ attached to it at B and C. It passes round a small smooth peg at D carrying a weight of $300\text{ N}$ at the free end E as shown in Fig. 1. If, in the equilibrium position, BC is horizontal and AB and CD make $150^\circ$ and $120^\circ$ with BC, find (i) Tensions in the portions AB, BC and CD of the string and (ii) Magnitudes of $W_1$ and $W_2$.

An effort of $200\text{ N}$ is required just to move a certain body up an inclined plane of angle $15^\circ$, the force acting parallel to the plane. If the angle of inclination of the plane is made $20^\circ$, the effort required, again applied parallel to the plane, is found to be $230\text{ N}$. Find the weight of the body and the coefficient of friction.

For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. (Note: A and B are hinge and roller supports, respectively)

Determine the coordinates of the centroid of the shaded area.

State the Hooke's law and draw the typical stress-strain curve for a ductile and brittle material.

Three cylinders weighing $100\text{ N}$ each and of $80\text{ mm}$ diameter are placed in a channel of $180\text{ mm}$ width as shown in Fig. 2. Determine the pressure exerted by (i) the cylinder A on B at the point of contact, (ii) the cylinder B on the base and (iii) the cylinder B on the wall.

Mention the statement of the first law and the second law of thermodynamics with examples.

What are the three modes of heat transfer? Explain each briefly.