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GATE 2019: Part Test-2

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Question 1

A ladder AB is placed at the wall as shown in the figure below touch the wall at point A and the floor at point B. The ladder is of length 5 m. There is no friction at the wall and the floor, assuming point A and point B moves only in vertical and horizontal directions only. Find the ratio of velocities of A and B when the ladder is at the given position as shown in the figure

Question 2

In a spring mass system, The mass is 0.9 kg and the stiffness of the spring is 1kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value, what is the damping coefficient of the damper?

Question 3

For a plane surface emitting radiation, the view factor of the plane surface with itself is

Question 4

Which is true for sequence of the thermal conductivity_____.?

Question 5

A flexible (8 × 19) steel wire rope of 40 mm diameter is used with 2 m diameter hoist drum to lift a load. The diameter of the wire may be taken as 0.05 d, where, d is the diameter of wire rope. Modulus of elasticity of the entire rope is 84 × 103 N/m2. What will be the maximum bending stress (in MPa) in the wire rope ?

Question 6

A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in N) is

Question 7

A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is 150 kg-m2. On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is

Question 8

Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is

Question 9

The rod AB, of length 1 m, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along QP and QR. If the velocity VA of the slider at A is 2 m/s, the velocity of the midpoint of the rod at this instant is ________m/s.

Question 10

The cantilever beam, as shown in figure below is made up of mild steel. It has negligible weight and is carrying a mass M at its free end and it also resting an elastic support of stiffness K1 as shown. If K2 represents the bending stiffness of the beam, the natural frequency for the system will be

Question 11

A uniform rigid slenderbar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K = 2kN/m, C =500 Ns/m and the stiffness of the torsional spring Kθ is 1 kN/m/rad. Ignore the hinge dimensions.
Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME-28-Mar\GATE-ME-2003_files\image385.jpg
The un-damped natural frequency of oscillations of the bar about the hinge point is

Question 12

A coolant fluid at 30 °C flows over a heated flat plate maintained at a constant temperature of 110 °C. The boundary layer temperature distribution at a given location on the plate may be approximated as where y (in m) is the distance normal to the plate and T is in °C. If thermal conductivity of the fluid is 1.0 W/m-K, the local convective heat transfer coefficient at that location will be ____________ W/m2-K.

Question 13

A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.

Question 14

A flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces along its 3m long side. The free stream temperature and velocity of air are 20 °C and 7m/s. The total drag force acting on the plate is measured to be 1.86 N. The average heat transfer coefficient for the plate is ___________ W/m2-K.
[The properties of air at 20 °C temperature and 1 atmospheric pressure are, Prandtl number, Pr= 0.7309]

Question 15

The main trunk duct of an air conditioning system is rectangular in cross-section (400 mmDescription: Description: E:\Gate\SSC JE Mechanical Part 1\Made Easy Questions\08_Heat-Transfer_BLok_files\image001.png800mm) and has air at atmospheric pressure and at 200C temperature flowing with a velocity of 7 m/s. estimate the heat leaskage (W) per meter length per unit temperature difference. Relevant physical properties of air are:
Description: Description: E:\Gate\SSC JE Mechanical Part 1\Made Easy Questions\08_Heat-Transfer_BLok_files\image054.png
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Jan 22ESE & GATE ME