A force F is acting on a bent bar which is clamped at one end as shown in the figure.

The CORRECT free body diagram is

The cross-section of two solid bars made of the same material is shown in the figure. The square cross-section has flexural (bending) rigidity EI₁, while the circular cross-section has flexural rigidity EI₂. Both sections have the same cross-sectional area. The ratio I₁/I₂ is

The state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).

The components (τ_xx, τ_yy, τ_xy) are given by

A rigid link PQ is undergoing plane motion as shown in the figure (V_P and V_Q are non-zero). V_QP is the relative velocity of point Q with respect to point P

Which one of the following is TRUE?

A channel of width 450 mm branches into two sub-channels having width 300 mm and 200 mm as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is 0.9 m³/s and the velocity in the sub-channel of width 200 mm is 3 m/s, the velocity in the sub-channel of width 300 mm is ______m/s

Assume both inlet and otlet to be at the same elevation.

Steady one-dimensional heat conduction takes place across the faces 1 and 3 of a composite slab consisting of slabs A and B in perfect contact as shown in the figure, where k_A, k_B denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature T₂ (in °C) is _______

The blade and fluid velocities for an axial turbine are shown in the figure.

The magnitude of absolute velocity at entry is 300 m/s at an angle of 65° to the axial direction, while the magnitude of the absolute velocity at exit is 150 m/s. The exit velocity vector has a component in the downward direction. Given that the axial (horizontal) velocity is the same at entry and exit, the specific work (in kJ/kg) is ______ 

Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminium. The shape of the cavity is a cylinder with 15 mm diameter. The size of the moulds are such that the outside temperature of the moulds do not increase appreciably beyond the atmospheric temperature during solidification. The sequence of solidification in the mould from the fastest to slowest is

(Thermal conductivities of steel, copper and aluminium are 60.5, 401 and 237 W/m-K, respectively.

Specific heats of steel, copper and aluminium are 434, 385 and 903 J/kg-K, respectively.

Match the following part programming codes with their respective functions

The value of the line integral \(\mathop \smallint \limits_C^{} \bar F\;.\;\bar r'ds\), where C is a circle of radius \( {\frac{4}{{\sqrt \pi }}} \) units is ________

An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is __________

A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in the figure. The speed v of the disc when it reaches position B is _________ m/s.

Acceleration due to gravity (g) = 10 m/s²

A rigid rod (AB) of length L = √2 m is undergoing translational as well as rotation motion in the x-y plane (see the figure). The point A has the velocity V₁ = î + 2ĵ m/s. The end B is constrained to move only along the x direction.

The magnitude of the velocity V₂ (in m/s) at the end B is _________

A square plate of dimension L × L is subjected to a uniform pressure load P = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa.

A beam of length L is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is EI. The reaction at the simple support at the right end is

Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses m₁ is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider m = 1 kg, e = 50 mm, e₁ = 20 mm, b = 0.3 m, a = 2 m and a₁ = 2.5 m. For the system to be dynamically balanced, m₁ should be _______ kg.

A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of \(\sqrt {\frac{{3k}}{m}} ,\) the ratio of the amplitude of steady state response to the static deflection of the spring is _______

A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is 25 mm². A torque T = 200 N-m is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is __________ MPa.

The water jet exiting from a stationary tank through a circular opening of diameter 300 mm impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is _________ kN. Density of water is 1000 kg/m³.(Take g = 10m/s2)

For a two-dimensional flow, the velocity field is \(\vec u = \frac{x}{{{x^2} + {y^2}}}\hat i + \frac{y}{{{x^2} + {y^2}}}\hat j,\) where î and ĵ are the basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below.

basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below.

1) The flow is incompressible.

2) The flow is unsteady.

3) y-component of acceleration, \({a_y} = - \frac{y}{{{{\left( {{x^2} + {y^2}} \right)}^2}}}\)

4) x-component of acceleration, \({a_x} = \frac{{ - \left( {x + y} \right)}}{{{{\left( {{x^2} + {y^2}} \right)}^2}}}\)

In the vapour compression cycle in the figure, the evaporating and condensing temperatures are 260 K and 310 K, respectively. The compressor takes in liquid-vapour mixture (state 1) and isentropically compresses it to a dry saturated vapour condition (state 2). The specific heat of the liquid refrigerant is 4.8 kJ/kg-K and may be treated as constant. The enthalpy of evaporation for the refrigerant at 310 K is 1054 kJ/kg.

The difference between the enthalpies at state points 1 and 0 (in kJ/kg) is ___________

Spot welding of two steel sheets each 2 mm thick is carried out successfully by passing 4 kA of current for 0.2 seconds through the electrodes. The resulting weld nugget formed between the sheets is 5 mm in diameter. Assuming cylindrical shape for the nugget, the thickness of the nugget is _______ mm.

Two optically flat plates of glass are kept at a small angle θ as shown in the figure. Monochromatic light is incident vertically.

A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts I and II are Rs. 40 and Rs. 100, respectively. The maximum profit per week of the firm is Rs. ________