ME GATE 2016 - Online Test
Q1. The cross sections of two hollow bars made of the same material are
concentric circles as shown in the figure. It is given that r3> r1 and
r4> r2, and that the areas of the cross-sections are the same. J1 and J2 are the torsional rigidities of the bars on the left and right,
respectively. The ratio J2/J1 is
Answer : Option A
Explaination / Solution:
Torsional rigidity for any Shaft is given by,
J = GIP
Or J ฮฑ IP (Polar moment of Inertia)
And for a hollow shaft,
Q2. A plastic sleeve of outer radius r0 = 1 mm covers a wire (radius
r = 0.5 mm) carrying electric current. Thermal conductivity of the
plastic is 0.15 W/m-k. The heat transfer coefficient on the outer
surface of the sleeve exposed to air is 25 W/m2-K. Due to the
addition of the plastic cover, the heat transfer from the wire to the
ambient will
Answer : Option A
Explaination / Solution:
r = 0.5 mm, r0 = 1 mm.
Given, the wire is like a cylinder. Hence, critical radius of insulation is
Now if we add insulation (plastic cover), the heat transfer will
increase.
Q3. A cantilever beam having square cross-section of side a is subjected
to an end load. If a is increased by 19%, the tip deflection decreases
approximately by
Answer : Option D
Explaination / Solution:
From the deflection formula, for cantilever beam having point load at
its free end,
Hence, decrement in the deflection in percentage will be
Q4. The INCORRECT statement about regeneration in vapor power
cycle is that
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. The spring constant of a helical compression spring DOES NOT
depend on
Answer : Option B
Explaination / Solution:
The spring constant (k) for the compression helical spring is given
by,
So, K is dependent on wire diameter, number of active coils, modulus
of rigidity, coil diameter, but does not depends on the martial
strength.
Q6. The figure below represents a triangle PQR with initial
coordinates of the vertices as P(1,3),Q(4,5) and R(5,3.5). The triangle
is rotated in the X-Y plane about the vertex P by angle ฮธ in clockwise
direction. If sinฮธ= 0.6 and cosฮธ= 0.8, the new coordinates of the
vertex ๐ are
Answer : Option A
Explaination / Solution:
Since the triangle is rotated in CW direction, hence, for the new point
Qโ (x,y),
x > 4 and y < 5 __________(1)
and PQ = PQโ or QR = QโRโ
Now we can get the answer easily by checking the option
Q7. A two-member truss PQR is supporting a load W. The axial
forces in members PQ and QR are respectively
Answer : Option B
Explaination / Solution:
FBD for the point Q is given by,
Q8. In the gear train shown, gear 3 is carried on arm 5. Gear 3
meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and
4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4
rotates with an angular velocity of 100 rpm in the counter clockwise
direction, the angular speed of arm 5 (in rpm) is
Answer : Option C
Explaination / Solution:
Given (taking CW as positive)
Q9. A solid disc with radius a is connected to a spring at a point d
above the center of the disc. The other end of the spring is fixed to the
vertical wall. The disc is free to roll without slipping on the ground.
The mass of the disc is M and the spring constant is K. The polar
moment of inertia for the disc about its center is j = Ma2/2
The natural frequency of this system in rad/s is given by
Answer : Option C
Explaination / Solution:
No Explaination.
Q10. The principal stresses at a point inside a solid object are ฯ1 =
100 MPa, ฯ2 = 100 MPa and ฯ3 = 0MPa. The yield strength of the
material is 200 MPa. The factor of safety calculated using Tresca
(maximum shear stress) theory is nT and the factor of safety
calculated using von Mises (maximum distortional energy) theory is
nV. Which one of the following relations is TRUE?
Answer : Option A
Explaination / Solution:
No Explaination.
