GATE 2017-2018 :: GATE Mechanical
- If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is
- A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rockerrocker) mechanism is
- Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is
- Choose the CORRECT set of functions, which are linearly dependent.
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The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.
where S is the sphere x2 + y2 + z2 = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is - The function f (t ) satisfies the differential equation d2f/dt2 + f = 0 and the auxiliary conditions, f(0) = 0, df/dt(0) = 4. The Laplace transform of f (t) is given by
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Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:Specific enthalpy (kJ/kg) Velocity (m/s)Inlet steam condition 3250 180Exit steam condition 2360 5The rate of heat loss from the turbine per kg of steam flow rate is 5 kW. Neglecting changes in potential energy of steam, the power developed in kW by the steam turbine per kg of steam flowrate, is
- Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is 20 mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter in mm of the stream 0.5 m below the tap is approximately
- A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat transfer coefficient h = 20 W/m2K. The thermo-physical properties of steel are: density Ï = 7800 kg/m3, conductivity k = 40 W/mK and specific heat c = 600 J/kgK. The time required in seconds to cool the steel ball in air from 1030°C to 430°C is
- A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ± 2%, the mass moment of inertia of the flywheel in kg-m2 is
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