Quiz: Mechanical Engineering

Exam: GATE

Topic: Miscellaneous

Each question carries 2 mark

Negative marking: 1/3 mark

Time: 20 Minutes

Q1. A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the barrel is 3m/s, while the barrel is swinging upwards with a constant angular velocity of 2rad/s the magnitude of the absolute velocity of the shell is

(a) 3 m/s

(b) 4 m/s

(c) 5 m/s

(d) 7 m/s

Q2. A thin walled spherical shell is subjected to an internal pressure if the radius of the shell is increases by 1% and the thickness is reduced by 1% with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

(a) 0

(b) 1

(c) 1.08

(d) 2.02

Q3. Mobility of a statically indeterminate structure is

(a) ≤ -1

(b) 0

(c) 1

(d) ≥ 2

Q4. In the figure shown, the spring deflects by δ to position A (the equilibrium position) when a mass m is kept on it. During free vibration, the mass is at position B at some instant. The change in potential energy of the spring mass system from position a to position B is

(a) 1/2 kx²

(b) 1/2 kx^2-mgx

(c) 1/2 k(x+δ)

(d) 1/2 kx^2+mgx

Q5. For the three bolt System shown in the figure, the bolt material has shear yield strength 200 MPa. For a factor of safety of 2, minimum metric specification required for the bolt is

(a) M 8

(b) M 10

(c) M 12

(d) M 16

Q6. The velocity components in the x and y direction of a two-dimensional potential flow are u and v, respectively. then ∂u/∂x, is equal to

(a) ∂V/∂x

(b) -∂V/∂x

(c) ∂V/∂y

(d) -∂V/∂y

Q7. A long glass cylinder of inner diameter = 0.03 m and outer diameter = 0.05m carries hot fluid inside if the thermal conductivity of glass = 1.05 W/mK, the thermal resistance (K/W) per unit length of the cylinder is

(a) 0.031

(b) 0.077

(c) 0.17

(d) 0.34

Q8. A steam turbine receives steam steadily at 10 bar with a enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. the work output is 250 kJ\kg. the changes in kinetic and potential energies are negligible the heat transfer from the turbine casing to the surroundings is equal to

(a) 0 kJ

(b) 50 kJ

(c) 150 kJ

(d) 250 kJ

Q9. Using direct extrusion process, a round billet of 100 mm length and 50 mm diameter is extruded. Considering an ideal deformation process (no friction and no redundant work) extrusion ratio 4 and average flow stress of material 300 MPa, the pressure (MPa) on the ram will be

(a) 416

(b) 624

(c) 700

(d) 832

Q10. The component development and manufacturing activities when assisted by a computer area: computer aided graphics (CAG), CAD, CAM, CAPP and computer aided quality control (CAQC). The most appropriate sequence of theses activities is

(a) CAD-CAG-CAPP-CAM-CAQC

(b) CAG-CAD-CAM-CAPP-CAQC

(c) CAD-CAG-CAPP-CAQC-CAM

(d) CAD-CAPP-CAG-CAM-CAQC

Solutions

S1. Ans.(c)

Sol. V_B=rω=2×2=4 m\/sec

V_SB= velocity of shell w.r.t. to barrel = 3m/sec

As shell is in barrel, the net velocity of shell

⇒(V_S ) ⃗=(V_B ) ⃗+(V_SB ) ⃗

⇒as (V_B ) ⃗ and (V_SB ) ⃗ are perpendicular

|(V_S ) ⃗ |=√((3)^2+(4)^2 )

=5m\/sec

S2. Ans.(d)

Sol. Hoop stress = pd/4t

P = internal pressure

d = diameter of shell

t = thickness of shell

now σ’ = pd’/4t’

d’ = 1.01d and t’ = 0.99 t

∵ σ’ = (P×1.01d)/(4×0.99 t)=1.0202σ

% change =(σ^’-σ)/σ×100

=(1.0202-1)σ/σ×100

=2.02 %

S3. Ans.(a)

Sol. Mobility or degree of freedom for a statically indeterminate structure is always less than zero.

i.e. F < 0

∵ only option (A) is negative value

∵ F ≤ -1

S4. Ans.(a)

Sol. ∆ (PE) = (PE)_B-(PE)_A

=1/2 k(x+δ)^2+0 [1/2 kδ^2+mgx ]

Taking reference datum at position B. At equilibrium position i.e., at a

mg=kδ

∆(PE)=1/2 kx^2+1/2 kδ^2+xkδ-1/2 kδ^2-mgx

As mg = kδ

∆(PE)=1/2 kx^2+1/2 kδ^2+mgx-1/2 kδ^2-mgx

=1/2 kx^2

S5. Ans.(b)

Sol.

P=τ_y/F_s ×π/4 d^2×m

⇒19000=(200×10^6)/2×π/4×d^2×3

d=8.98×10^(-3) m=8.98 mm

So, M10

S6. Ans.(d)

Sol. for two dimensional flow, continuity equation should be satisfied.

i.e,

∂u/∂x+∂v/∂y=0

∵∂u/∂x= -∂v/∂y

S7. Ans.(b)

Sol. Given Data;

d_1=0.03 m

r_1=d_1/2-0.03/2=0.015 m

d_2=0.05 m

r_2=0.5/2= 0.025 m

K=1.05 W\/mk

Thermal resistance

R_T =1/2πkl log_e (0.025/0.015)

=0.077 W\/m

S8. Ans.(b)

Sol. Given data;

P_1=10 bar,h_1=3000 kJ\/kg,P_2=1bar,h_2=2700 kJ\/kg,W=250 kJ\/kg ;Q= ?

The steady flow energy equation for unit mass flow rate,

h_1+(V_1^2)/2+gz_1+q=h_2+(V_2^2)/2+gz_2+W

Change in kE and PE are negligible

h_1+q=h_2+w

3000+q=2700+250

pr.q= -50 kJ\/kg

The heat transfer from the casing of the turbine surreally is equal to 50 kJ/kg

S9. Ans.(a)

Sol. l_0=100,σ_y=300 MPa,d_o=50 mm

E.R = A_0/A_1 =4

A_O=1962.5 mm^2

A_1=A_0 \/4=(π\/4(50)^2)/4=490 mm^2

Extrusion pressure = 300 ln (extrusion ratio)

= 415.8 MPa.

S10. Ans.(a)

Sol. Development activity starts with design using CAD, CAG is used for producing production drawing, CAPP is used for process planning followed for CAM and CAQC.