A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30° with the vertical. The magnitude of force F (in N) is _______.

A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is

The cross sections of two hollow bars made of the same material are concentric circle as shown in the figure. It is given that r₃ > r₁ and r₄ > r₂, and that the areas of the cross-sections are the same. J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratio J₂/J₁ is

The instantaneous stream-wise velocity of a turbulent flow is given as follows:

\(u\left( {x,\;y,\;z,\;t} \right) = \bar u\;\left( {x,\;y,\;z} \right) + u'\left( {x,\;y,\;z,\;t} \right)\)

Which of the following statements are TRUE with respect to heat and work?

(i) They are boundary phenomena

(ii) They are exact differentials

Propane (C₃H₈) is burned in an oxygen atmosphere with 10% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of CO in the products is _______.

Match the following

The value of the integral

\(\mathop \smallint \limits_{ - \infty }^\infty \frac{{\sin x}}{{{x^2} + 2x + 2}}dx\)

Gauss-Seidel method is used to solve the following equations (as per the given order):

x₁ + 2x₂ + 3x₃ = 5

2x₁ + 3x₂ + x₃ = 1

3x₁ + 2x₂ + x₃ = 3

A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is 0.25. The string can withstand a maximum force of 20 N. The maximum value of the mass (m) for which the string will not break and the block will be in static equilibrium is ______ kg.

Take cos θ = 0.8 and sin θ = 0.6

Acceleration due to gravity g = 10 m/s²

A two-member truss PQR is supporting a load W. The axial forces in members PQ and QR are respectively

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections AB and BC are 3E and E, respectively.

For the deflection at C to be zero, the ratio P/F is _________

The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in mm⁴) of this cross-section about its base is _______

A simply-supported beam of length 3L is subjected to the loading shown in the figure.

It is given that P = 1 N, L = 1 m and Young’s modulus E = 200 GPa. The cross-section is a square with dimension 10 mm × 10 mm. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of 1.5L from the left end is ___________

A slider crank mechanism with crank radius 200 mm and connecting rod length 800 mm is shown. The crank is rotating at 600 rpm in the counterclockwise direction. In the configuration shown, the crank makes an angle of 90° with the sliding direction of the slider, and a force of 5 kN is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in kN-m) is _______

In the gear shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4 rotates with an angular velocity of 100 rpm in the counter-clockwise direction, the angular speed of arm 5 (in rpm) is

A solid disc with radius a is connected to a spring at a point d above the centre of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is M and the spring constant is K. The polar moment of inertial for the disc about its centre is J = Ma²/2

The natural frequency of this system in rad/s is given by

An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil (specific gravity = 0.8) and pipe B is carrying water. The densities of air and water are 1.16 kg/m3 and 1000 kg/m3, respectively. The magnitude of pressure difference between pipes A and B is __________ kPa.

Acceleration due to gravity g = 10 m/s2.

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A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is U_a. The velocity profile at the inlet a-b is uniform, while that at a downstream location c-d is given by \(u = {U_0}\left[ {2\left( {\frac{y}{\delta }} \right) - {{\left( {\frac{y}{\delta }} \right)}^2}} \right].\)

The ratio of the mass flow rate, ṁ_bd, leaving through the horizontal section b-d to that entering through the vertical section a-b is _________

An infinitely long furnace of 0.5 m × 0.4 m cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature T₁ = T₃ = 927°C while the side walls are at temperature T₂ = T₄ = 527°C. The view factor, F_1-2 is 0.26.

The net radiation heat loss or gain on side 1 is __________ W/m.

Stefan-Boltzmann constant = 5.67 × 10^-8 W/m²-K⁴

In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at 3 MPa and 350^oC. The condenser pressure is 75 kPa. The thermal efficiency of the cycle is ______ percent.

Given data:

For saturated liquid, at P = 75 kPa, h_f = 384.39 kJ/kg, v_f = 0.001037 m³/kg, s_f = 1.213 kJ/kg-K

At 75 kPa, h_fg = 2278.6 kJ/kg, s_fg = 6.2434 kJ/kg-K

A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR, RS with coordinates P(0, 0), Q(0.2, 100), R(0.6, 140) and S(0.8, 130). ‘Q’ is the yield point. ‘R’ is the UTS point and ‘S’ the fracture point

The toughness of the material (in MJ/m³) is ______

Heat is removed from a molten metal of mass 2 kg at a constant rate of 10 kW till it is completely solidified. The cooling curve is shown in the figure.

Assuming uniform temperature throughout the volume of the metal during solidification, the latent heat of fusion of the metal (in kJ/kg) is ________

The tool life equation for HSS tool is VT^0.14 f^0.7d^0.4 = Constant. The tool life (T) of 30 min is obtained using the following cutting conditions:

V = 45 m/min, f = 0.35 mm, d = 2.0 mm

The figure below represents a triangle PQR with initial coordinates of the vertices as P(1, 3), Q(4, 5) and R(5, 3.5). The triangle is rotated in the X-Y plane about the vertex P by angle θ in clockwise direction. If sin θ = 0.6 and cos θ = 0.8, the new coordinates of the vertex Q are

Maximize Z = 15X₁ + 20X₂ subject to

12X₁ + 4X₂ ≥ 36

12X₁ – 6X₂ ≤ 24

X₁, X₂ ≥ 0