Mechanical Engineering Gate Yearwise

Mechanical Engineering GATE 2014 Set-2 Questions with Answer

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Ques 1 Dynamics

Consider a flywheel whose mass M is distributed almost equally between a heavy, ring-like rim of radius R and a concentric disk-like feature of radius R/2. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for α, if the moment of inertia of the flywheel about its axis of rotation is expressed as αMR², is _______

0.56 is the correct answer.

Ques 2 Dynamics of Machines

A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s². When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s²) of the end P is _______

40 is the correct answer.

Ques 3 Engineering Mathematics

One of the eigenvectors of the matrix is

Ques 4 Engineering Mathematics

is equal to

0.5

Ques 5 Engineering Mathematics

Curl of vector F = x²z² î - 2xy²z ĵ + 2 y²z³k̂ is

-2y²zk̂ + 2x²z ĵ + (4yz³+2xy²) î

2z²k̂ − 2xz ĵ + (3y²−4y) î

2xz² î - 4xyz ĵ + 6y²z² k̂

2xz² î + 4xzy ĵ + 6y²z² k̂

Ques 6 Engineering Mathematics

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x,y) + iv(x,y), where i = √−1. If u(x,y) = 2xy, then v(x,y) must be

x² + y² + constant

x² − y² + constant

−x² + y² + constant

−x² − y² + constant

Ques 7 Engineering Mathematics

The general solution of the differential equation dy/dx = cos(x+y), with c as a constant, is

x+c = y + sin(x+y)

y + c= tan((x+y)/2)

x+ c= cos((x+y)/2)

x+c = tan((x+y)/2)

Ques 8 Engineering Mechanics

A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is _______

20 is the correct answer.

Ques 9 Engineering Mechanics

A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s²) of the truck such that the crate does not slide down is _______

1.1 is the correct answer.

Ques 10 Fluid Mechanics

For an incompressible flow field, V⃗, which one of the following conditions must be satisfied?

∇·V⃗ = 0

∇×V⃗ = 0

V⃗ ·∇V⃗ = 0

∂V⃗/∂t + V⃗ ·∇V⃗ = 0

Ques 11 Fluid Mechanics

The difference in pressure (in N/m²) across an air bubble of diameter 0.001 m immersed in water (surface tension = 0.072 N/m) is _______

288 is the correct answer.

Ques 12 Fluid Mechanics

Water flows through a 10 mm diameter and 250 m long smooth pipe at an average velocity of 0.1 m/s. The density and the viscosity of water are 997 kg/m³ and 855×10⁻⁶ N·s/m², respectively. Assuming fully-developed flow, the pressure drop (in Pa) in the pipe is _______

6860 is the correct answer.

Ques 13 Fluid Mechanics

Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is _______

13.7 is the correct answer.

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