Entrance exam Ph.D Mechanical Questions

I am interested to Ph.D Mechanical IIT Bombay so, want the question paper of that will you please provide me that????

[Kiran Chandar]

As you want to do Ph.D Mechanical from IIT Bombay so, for you here I am providing you the question paper of that.

Here is an attachment for the question paper and some of the questions are given below:

1. A stepped circular rod of equal step size l and cross-section A and 2A connects two rigid and
fixed plates, which form the walls of a channel carrying fluid in a process plant. The material
modulus of elasticity of the rod is E and coefficient of thermal expansion is α. The fluid flowing
raises the temperature of the rod uniformly to level T above the room temperature. At room
temperature, the rod is free of any load.Using the equilibrium and compatibility conditions, it is
possible to calculate the stresses in each segment of the rod. The equilibrium condition means that sum of all forces acting on the component is zero. The compatibility refers to the constraint on the deformation.

2. A circular bar with fixed ends carries a wheel of mass m (kg) with polar mass momentof
Inertia J (kgm2). The polar area moment of inertia of the bar cross-section is I (m4). The
Wheel is located at the centre of the bar of length l (m); the modulus of rigidity of the bar
Material is G (N/m2). The thickness of the wheel b (m) is very small compared to 0.5l.
The wheel is given a small rotation θ=θo from its rest position (θ=0o) and let go.Applying
D’Alembert’s principle and the condition of equilibrium, it is possible to obtain
The equation of motion of the wheel. According to the D’Alembert’s principle, the inertia force acts in the direction opposite to the direction of acceleration. In the above case that inertia torque is equal to ̈ .
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