Mechanical Engineering GATE 2024 Questions with Answer

Ques 53 Mathematics

The velocity field of a two-dimensional, incompressible flow is given by
𝑉⃗ = 2 sinh 𝑥 𝑖̂+ 𝑣(𝑥, 𝑦) 𝑗̂
where 𝑖̂ and 𝑗̂ denote the unit vectors in 𝑥 and 𝑦 directions, respectively. If 𝑣(𝑥, 0) = cosh 𝑥, then 𝑣(0, −1) is

Ques 54 Mechanical Vibration

A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping (in N.s/m) is

Ques 55 Mechanical Vibration

A vibratory system consists of mass m, a vertical spring of stiffness 2k and a horizontal spring of stiffness k. The end A of the horizontal spring is given a horizontal motion x_A = a sin ωt. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume m = 10 kg, k = 1.5 kN/m and neglect friction. The magnitude of the critical driving frequency for which the oscillations of mass m tend to become excessively large is _______________ rad/s (answer in integer).

Ques 56 Strength of Materials

Which of the following beam(s) is/are statically indeterminate?

A

B

C

D

Ques 57 Strength of Materials

A horizontal beam of length 1200 mm is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of the maximum bending moment acting on the beam is _______________ N.m. (round off to 1 decimal place).

Ques 58 Theory of Machines

The Levai type-A train illustrated in the figure has gears with module m = 8 mm/tooth. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at 20 rev/min counter-clockwise. The magnitude of the angular velocity of the arm is _______________ rev/min. (rounded off to 2 decimal places)

Ques 59 Theory of Machines

At the instant when OP is vertical and AP is horizontal, the link OD is rotating counterclockwise at a constant rate ω = 7 rad/s. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of the angular velocity of link ABC for this instant is _______________ rad/s (rounded off to 2 decimal places).

Ques 60 Theory of Machines

A band brake shown in the figure has a coefficient of friction of 0.3. The band can take a maximum force of 1.5 kN. The maximum braking force (F) that can be safely applied is _______________ N (rounded off to the nearest integer).

Ques 61 Thermodynamics

A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is

Ques 62 Thermodynamics

Which one of the following statements regarding a Rankine cycle is FALSE?

Ques 63 Thermodynamics

Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at 100 kPa and 300 K and exits the compressor at 600 kPa and 550 K. The air exits the combustion chamber at 1250 K and exits the adiabatic turbine at 100 kPa and 800 K. The exhaust air from the turbine is used to preheat the air in the regenerator. The exhaust air exits the regenerator (state 6) at 600 K. There is no pressure drop across the regenerator and the combustion chamber. Also, there is no heat loss from the regenerator to the surroundings. The ratio of specific heats at constant pressure and volume is c_p / c_v = 1.4. The thermal efficiency of the cycle is % __________. (answer in integer).

Ques 64 Thermodynamics

A piston-cylinder arrangement shown in the figure has a stop located 2 m above the base. The cylinder initially contains air at 140 kPa and 350 o C and the piston is resting in equilibrium at a position which is 1 m above the stops. The system is now cooled to the ambient temperature of 25 o C. Consider air to be an ideal gas with a value of gas constant R = 0.287 k J / ( k g. K ). The absolute value of specific work done during the process is ______.(rounded off to 1 decimal place)

Ques 65 Thermodynamics

A heat pump (H.P.) is driven by the work output of a heat engine (H.E.) as shown in the figure. The heat engine extracts 150 kJ of heat from the source at 1000 Κ. The heat pump absorbs heat from the ambient at 280 K and delivers heat to the room which is maintained at 300 K. Considering the combined system to be ideal, the total amount of heat delivered to the room together by the heat engine and heat pump is __________ kJ (answer in integer).