Mechanical Engineering Gate 2014 Set-3 Questions with Answer

Ques 40 GATE 2014 SET-3

A cylindrical riser with diameter d and height h, is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio h:d is

Ques 41 GATE 2014 SET-3

The diameter of a recessed ring was measured by using two spherical balls of diameter d₂=60 mm and d₁=40 mm as shown in the figure. The distance H₂=35.55 mm and H₁=20.55 mm. The diameter (D, in mm) of the ring gauge is ________.

Ques 42 GATE 2014 SET-3

Which pair of following statements is correct for orthogonal cutting using a single-point cutting tool?
P. Reduction in friction angle increases cutting force
Q. Reduction in friction angle decreases cutting force
R. Reduction in friction angle increases chip thickness
S. Reduction in friction angle decreases chip thickness

Ques 43 GATE 2014 SET-3

For spot welding of two steel sheets (base metal) each of 3 mm thickness, welding current of 10000 A is applied for 0.2 s. The heat dissipated to the base metal is 1000 J. Assuming that the heat required for melting 1 mm³ volume of steel is 20 J and interfacial contact resistance between sheets is 0.0002 Ω, the volume (in mm³) of weld nugget is ________.

Ques 44 GATE 2014 SET-3

Consider an objective function Z(x₁, x₂) = 3x₁ + 9x₂ and the constraints
x₁ + x₂ ≤ 8,
x₁ + 2x₂ ≤ 4,
x₁ ≥ 0, x₂ ≥ 0.
The maximum value of the objective function is _______

Ques 45 GATE 2014 SET-3

Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

Ques 46 GATE 2014 SET-3

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is 100 MPa. If the yield, ultimate, and corrected endurance strength of the shaft material are 300 MPa, 500 MPa and 200 MPa respectively, then the factor of safety for the shaft is _______

Ques 47 GATE 2014 SET-3

Two solid circular shafts of radii R₁ and R₂ are subjected to same torque. The maximum shear stresses developed in the two shafts are τ₁ and τ₂. If R₁/R₂ = 2, then τ₁/τ₂ is _______

Ques 48 GATE 2014 SET-3

Which one of following is NOT correct?

Ques 49 GATE 2014 SET-3

A force P is applied at a distance x from the end of the beam as shown in the figure. What would be the value of x so that the displacement at ‘A’ is equal to zero?

Ques 50 GATE 2014 SET-3

Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by t, lying in the interval 0 to 2π, is associated with the maximum translation of the follower during one full rotation of the cam rotating about the center at (x, y) = (0, 0)?

Ques 51 GATE 2014 SET-3

A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is _______

Ques 52 GATE 2014 SET-3

Gear 2 rotates at 1200 rpm counterclockwise and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The number of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30 respectively. The angular speed of Gear 5 is