NHPC JE'21 ME: Daily Practices Quiz. 25-Oct-2021

Quiz: Mechanical Engineering
Exam: NHPC JE
Topic: Miscellaneous

Each question carries 1 mark
Negative marking: 1/4 mark
Time: 6 Minutes

Q1. The elongation in a bar of circular cross-section, having a length L subjected to a tensile load P and tapering uniformly from a diameter d_1 at one end to a diameter d_2 at the other end, is given by
(a) PL/(4Ed_1 d_2 )
(b) πPL/(Ed_1 d_2 )
(c) πPL/(4Ed_1 d_2 )
(d) 4PL/(πEd_1 d_2 )

Q2. A cylindrical rod which has cross-sectional area 200 ×10^(-6) m² is subjected to a tensile force. Based on the Tresca criterion, if the uniaxial yield stress of the material is 100 MPa, the failure load is
(a) 10 KN
(b) 20 KN
(c) 100 KN
(d) 200 KN

Q3. A key which is square in shape is used to transmit torque (T) from the shaft to the hub. The relationship between induced compressive stress (σc) and shear stress (τ) is
(a) σ=τ
(b) σ=2τ
(c) σ=τ/2
(d) σ=τ/4

Q4. A cotter joint is used to connect two rods which are subjected to
(a) Compressive stress only
(b) Tensile as well as Compressive stress only
(c) Tensile only
(d) Shear only

Q5. The dynamic load on a gear is due to
1. inaccuracies of tooth spacing
2. irregularities in tooth profile
3. deflection of the teeth under load
4. type of service (i.e., intermittent, one shift per day, continuous per day)
Which of these statements are correct?
(a) 1, 2 and 3
(b) 2, 3 and 4
(c) 1, 3 and 4
(d) 1, 2 and 4

Q6. Consider the following statements:
A 20° stub tooth system is generally preferred in spur gears as it results in
1. Stronger teeth
2. Lesser number of teeth on the pinion
3. It is restrained to expand or contract freely
4. Reduction of interference
Which of these statements are correct?
(a) 1, 2 and 4
(b) 3 and 4
(c) 1 and 3
(d) 1, 2, 3 and 4

Solutions

S1. Ans.(d)
Sol. The elongation of circular cross-section tapering uniformly from a diameter d_1 at one end to a diameter d_2 at the other end subjected to tensile load P is

δL=4PL/(πd_1 d_2 E)
S2. Ans.(b)
Sol. We know that by Tresca Theory
τ_max=(σ_1-σ_2)/2 =σ_y/2
Since, uniaxial loading so σ_2=0
Therefore σ_1=σ_y (σ_1=force×area)
Force = 200 × 10^6×100×10^(-6) = 20kN

S3. Ans. (b)
Sol. Let torque transmitted by shaft is T, a is the side of the key and l be the length of the key.
Then tangential force acting on the key is
F=2T/d
Shear stress in square key

τ=(shear force)/(shear area of the key)=(2T/d)/al=2T/dal
Compressive stress in square key
σ=(compressive force)/(comressive area)=(2T/d)/(a/2 l)=4T/dal
Hence,
σ=2τ
S4. Ans. (b)
Sol. A cotter joint is used to connect to Co-axial rods, which are subjected to either axial tensile force or axial compressive force.
Cotter Joint are used in the following cases
(i) Foundation bolt
(ii) Joint between the piston rod and the tail or pump rod.
(iii) Joint between the slide spindle and the fork of the valve mechanism
(iv) Joint between the piston and the cross head of a steam Engine

S5. Ans.(a)
Sol. The dynamic load on gears is due to the following factors
(i) In inaccuracies in tooth profile
(ii) Errors in tooth spacing
(iii) Runout of the gear
(iv) Gear mesh stiffness variation as the gear teeth pass through the meshing cycle
(v) Inertia of rotational masses
(vi) Deflection of teeth
(vii) Stiffness of the rotating parts

S6. Ans.(a)
Sol. A 20° stub tooth system is generally preferred in spur gears as it results in
1. Stronger teeth.
2. Lesser number of teeth on the pinion.
3. Smaller interference.
4. Transmits very high load.