1. Calculate the moment of inertia and radius of gyration of a solid sphere of mass 10 kg and diameter 6.5m about its centroidal axis.
a) 2.055 m
b) 3.055 m
c) 4.055 m
d) 5.055 m
Explanation: I = 2/5 mr2 = 49 kgm2
k = 0.6325 x 3.25 = 2.055 m.
2. Calculate the work done per minute by a punch tool making 20 working strokes per min when a 30 mm diametre hole is punched in 5 mm thick plate with ultimate shear strength og 450 Mpa in each stroke.
a) 10.69 kNm
b) 20.69 kNm
c) 30.69 kNm
d) 40.69 kNm
Explanation: Force required to punch one hole = area shared x ultimate shear strength = пdt x Ss
Ss = п x 30 x 5 x 450/1000 = 212.05 kN
Work done/min = Average force x Thickness of plate x No. of holes/min
= 212.05/2 x 5/1000 x 20 = 10.69 kNm.
3. For driving a gramophone, which of the following governor is used?
a) Watt governor
b) Hartnell governor
c) Porter governor
d) Pickering governor
Explanation: For driving a gramophone a Pickering governor is used. It consists of three straight leaf springs arranged at equal angular intervals round the spindle. Its speed is controlled by dissipating excess kinetic energy.
4. The weights move inwards and the springs bend as they rotate about the spindle axis with increasing speed.
a) True
b) False
Explanation: For a Pickering governor, the weights move outwards and the springs bend as they rotate about the spindle axis with increasing speed. Hence, the given statement is false.
5. A Pickering governor is driving a gramophone. Each disc attached to the centre of a leaf spring has a mass of 20 g. The width of each spring is 5 mm and thickness of 0.125 mm. The effective length of each spring is 40 mm. The distance from the spindle axis to the centre of gravity of the mass when the governor is at rest, is 10 mm. Find the speed of the governor in rpm when the sleeve has risen to a height of 0.8 mm. (E = 210kN/mm2)
a) 2.675
b) 5.43
c) 51.0
d) 12.25
Explanation: I = bt3/12
=0.0008mm2
Length between fixed ends (L = 40-0.8 mm)
Calculating delta from central deflection will give
δ = 3.65 mm
3.65=0.51ω2
ω=2.675 rad/s.
6. A Pickering governor is driving a gramophone. Each disc attached to the centre of a leaf spring has a mass of 20 g. The width of each spring is 5 mm and thickness of 0.125 mm. The effective length of each spring is 40 mm. The distance from the spindle axis to the centre of gravity of the mass when the governor is at rest, is 10 mm, find the speed of the turntable in rpm if ratio of the governor speed to the turntable speed is 10.5.
a) 25.5
b) 2.43
c) 51.0
d) 12.25
Explanation: I = bt3/12
= 0.0008 (mm2)2
Length between fixed ends (L = 40-0.8 mm)
Calculating delta from central deflection will give
δ = 3.65 mm
3.65=0.51ω2
ω=2.675 rad/s
N = 25.5 rpm
N1 = 2.43 rpm.
7. From the following data calculate the speed of governor in rpm.
Dimensions of spring = 6mm wide, 0.12 mm thick and length = 48 mm
mass attached to each leaf at centre = 25g
Distance between spindle axis and C.O.M when the governor is at rest = 8mm
Sleeve lift = 0.6mm
E = 200 GN/mm2
a) 575
b) 625
c) 600
d) 550
Explanation: I = bt3/12
= 0.864×10-15 (m2)2
δ = 0.003464 m
= Fl3/192EI
ω=60.22 rad/s
N=575 rpm.
8. From the data given:
Dimensions of spring = 6mm wide, 0.12 mm thick and length = 48 mm
mass attached to each leaf at centre = 25g
Distance between spindle axis and C.O.M when the governor is at rest = 8mm
Sleeve lift = 0.6mm
E= 200 GN/mm2
Find the speed of the turntable in rpm if ratio of the governor speed to the turntable speed is 10.
a) 57.5
b) 62.5
c) 60
d) 55
Explanation: I = bt3/12
= 0.864×10-15 (m2)2
δ = 0.003464 m
= Fl3/192EI
ω=60.22 rad/s
N=575 rpm
N1= N/10
= 57.5 rpm.
9. In case of pickering governor, the central load is_______
a) Centripetal force
b) Centrifugal force
c) Torque
d) Normal reaction
Explanation: W = FC = m.ω2 (a + δ), this is the expression of the central load, hence the central load is the centrifugal force.
10. Porter governor is used to vary the speed of the turntable in a gramophone.
a) True
b) False
Explanation: Pickering governor is used to vary the speed of the turntable in a gramophone. Porter governor is used to regulate the speed of the engine.