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# Quiz: Mechanical Engineering 3rd June

Quiz: Mechanical Engineering
Exam: AE/JE
Topic: Miscellaneous

Each question carries 2 mark
Negative marking: 1/3 mark
Time: 15 Minutes

Q1. Grubler’s criterion is applicable for the mechanism with
(a) Zero degree of freedom
(b) Single degree of freedom
(c) Two degree of freedom
(d) More than two degree of freedom

Q2. In a slotted lever quick return mechanism, the crank length is 30 cm while the distance between centres of crank and slotted lever rotation is 60 cm. What is the ratio of cutting stroke time to return stroke time?
(a) 2
(b) 3
(c) 4
(d) 5

Q3. A point B on a rigid link AB moves with respect to A with angular velocity ω rad/s. The total acceleration of B with respect to A will be equal to
(a) Vector sum of radial component and Coriollis component
(b) Vector sum of tangential component and Coriollis component
(c) Vector sum of tangential component and radial component
(d) Vector difference of radial component and tangential component

Q4. A slider moving on a curved surface will have its instantaneous centre-
(a) at their point of contact
(b) at infinity
(c) at the center of curvature
(d) anywhere on the curved surface

Q5. In cycloidal motion of cam follower, the maximum acceleration of follower motion f_max at θ =ϕ/4 is
(a) (hπω^2)/(2ϕ^2 )
(b) (3hπω^2)/(2ϕ^2 )
(c) (2hπω^2)/ϕ^2
(d) (3hπω^2)/ϕ^2
Q6. The expression for COP of reversed Brayton cycle is (r_P is the pressure ratio)
(a) 1/(〖r_p〗^((γ-1)/γ)-1)
(b) 1/(〖r_p〗^γ-1)
(c) 1/〖r_p〗^((γ-1)/γ)
(d) 1/(〖r_p〗^((γ-1)/γ)+1)

Q7. If COP of a refrigerator is 5 and efficiency of a heat engine of the same temperature limit is 50%. Then what is the ratio of heat supplied to an engine to heat absorbed by the refrigerator from the space?
(a) 2.5
(b) 0.4
(c) 4
(d) 0.25

Q8. Which of the following is false statements?
Some of the methods used to reduce diesel smoke are as follows
(a) using additives in the fuel
(b) engine derating i.e. reducing the maximum flow of fuel
(c) increasing the compression ratio

Q9. Volumetric analysis of a certain flue gas gave CO_2 15%, O_2 5% and rest as N_2. The gas was at a temperature of 200℃ and a pressure of 5 bar. The partial pressure of N_2 in the flue gas is
(a) 250 kN/m^2
(b) 300 kN/m^2
(c) 350 kN/m^2
(d) 400 kN/m^2

Q10. The doublet is a special case of source and sink pair when:
(a) the source and sink are of equal strength.
(b) the source strength exceeds the sink strength.
(c) the source and sink coincide while moving along the axis.
(d) the source-sink pair of equal strength approach each other such that the product of strength and the distance remains constant

Solutions

S1. Ans (b)
Sol. We know that D.O.F. in plane according to Kutzbach’s equation,
▭(N=3(L-1)-2P_1-P_2 ) …………………….(1)
N→ No. of DOF
P₁→ No. of lower pair
P₂ → No. of higher pair
When higher pair (P₂) = 0, and N= 1
▭(1=3(L-1)-2P_1^ ) …………………………….(2)
This equation (2) is known as Grubler’s criterion.
S2. Ans (a)
Sol. We know that
Ratio=(Forward motion time)/(Return motion time)

``                           = 2α/2β=  α/β -------------- (1)``

From ∆ OO^’ A,
Sin r = OA/(OO^’ )
=30/60
=1/2
▭(r=30°)
Hence,
β+r+90°=180°
β=60°
From eqn. (1) Ratio =α/β=(180-β)/β
=120/60
▭(α/β=Ratio =2)

S3. Ans (c)
Sol. Total acceleration of point B with respect to point A is vector sum of radial component (a_r) and tangential component (a_t).

i.e. Total Acceleration of point B (a_R) =√(〖(a_r)〗^2+〖(a_t)〗^2 )

S4. Ans (c)
Sol. A slider moving on a curve surface will have its instantaneous center at the center of curvature.

S5. Ans (c)
Sol. Cycloidal cam motion is the most ideal for high speed follower motion.
For cycloidal motion of cam follower, the maximum acceleration of follower motion f_max at θ =ϕ/4 is (2hπω^2)/ϕ^2

S6. Ans (a)
Sol.
(〖COP)〗_(Reversed Brayton)=1/(〖r_p〗^((γ-1)/γ)-1)

Here, r_P is the pressure ratio.

S7. Ans (b)
Sol. Given,
(COP)_R=5
η_HE=0.5

η_HE=0.5=(T_2-T_1)/T_2 =W/Q_2 (Here, W_out=W_in=W )
W=0.5×Q_2…………….(1)
(COP)_R=5=T_1/(T_2-T_1 )=Q_1/W
W=Q_1/5……………………….(2)
Now comparing equation (1) and (2)
0.5×Q_2=Q_1/5
Q_2/Q_1 =1/2.5=0.4

S8. Ans (c)
Sol. Increasing the compression ratio is not recommended to reduce diesel smoke as it increases the weight of the engine and cost which is not worthy for reducing diesel smoke.

S9. Ans. (d)
Sol. Given,
No of moles of different gases as volumetric %
V_(CO_2 )=0.15
V_(O_2 )=0.05
V_(N_2 )=0.8
P_total=5 bar
Partial pressure of N_2 =V_(N_2 )/(V_(N_2 )+V_(CO_2 )+V_(O_2 ) )
=0.8/(0.8+0.15+0.05)×500=400 kN/m^2

S10. Ans (d)
Sol. The doublet forms when the source-sink pair of equal strength approach each other such that the product of strength and the distance remains constant. Doublet follows Laplace equation i.e. ∇^2∅=0

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