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GATE ME 2019: Topper's Quiz-9

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Question 1

Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0 in: cross-sectional area is 200 〖mm〗^2; Young's modulus E = 200 GPa. The force in the truss AB (in N) is _________.

Question 2

The magnitude (in KN) of force in the element BD for the truss shown below is ___.

Question 3

Air flows at the rate of

through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as

and assume inviscid incompressible flow. The change in pressure

(in kPa) between sections 1 and 2 is

Question 4

Three pipes of lengths 700m, 400m and 300m and of diameters 400mm, 300mm and 200mm respectively are connected in series. These pipes are to be replaced by a single pipe of length 1700m. Find the diameter of the single pipe.

Question 5

Determine the local Nusselt number for a fluid flowing over a plate having thermal diffusivity of 0.143X10-⁶, kinematic viscosity of 1.03X10-⁶ with a velocity of 0.6 m/s over a length of 2m.

Question 6

Find the time period for a lumped system to reach the average temperature of initial and surrounding temperature. The properties of the lumped system spherical in shape having diameter of 1.2mm are h= 85W/

K, 𝞺= 8500kg/

, Cp=320J/kgK.

Question 7

Find the standard deviation for the following forecasting data given below

Question 8

At a single server barber shop, the barber serves 8 customers per hour and arriving of customers at a rate of 5 per hour. Find the probability that at least 1 customer awaiting in the queue (upto three places of decimal)

Question 9

A torque of 10 kN-m is subjected to a shaft of material having its yield point of 350 MPa. The required diameter of shaft using maximum shear stress theory and maximum distortion energy theory respectively will be (Take factor of safety of 2.5)

Question 10

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 11

For shaft the allowable shear stress and the maximum allowable twist are 55 MN/m² and 0.3 deg/m. Diameter of shaft, below which the angle of twist, and not the maximum stress is the controlling factor in design of solid shaft in torsion is _________ mm. [Take, C_p = 80 GN/m²]

Question 12

The thickness of a metallic sheet is reduced from an initial value of 16 mm to a final value of 10 mm in one single pass rolling with a pair of cylindrical rollers each of diameter of 400 mm. The bite angle in degree will be

Question 13

Assume that the following specify a generalized linear programming problem
Maximize Z = 40x + 45y
Subject to:
x + y

80
x + 2y

90
x, y

0
Calculate the 2^nd feasible point by solving it by simplex method:

Question 14

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_____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

Question 15

Atmospheric air at 40℃ DBT & 50%RH is passed over a cooling coil at the rate of 600

/hr at exit from the coil. The air is saturated and its temperature is 8℃. The condensate also leaves at 8℃. Determine the amount of condensate leaving the coil/min. Assume specific heat of saturated steam 1.88kJ/kgK. Saturation pressure at DBT of 40℃ & 8℃ are 7.38kPa and 1.685kPa

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