Mechanical Engineering (ME) 2001 GATE Paper without solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


GATE ME - 2001
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 The divergence of vector r xi yj zk = + +
r r r r
is 
(a) i j k + +
r r r
(b) 3 (c) 0 (d) 1 
1.2 Consider the system of equations given below: 
2
2 2 5
x y
x y
+ =
+ =
This system has 
(a) one solution (b) no solution 
(c) infinite solutions (d) four solutions 
1.3 What is the derivative of ( ) at 0? f z x x = =
(a) 1 (b) -1 
(c) 0 (d) Does not exist 
1.4 The Gauss divergence theorem relates certain 
(a) surface integrals to volume integrals 
(b) surface integrals to line integrals 
(c) vector quantities to other vector quantities 
(d) line integrals to volume integrals 
1.5 For a spring-loaded roller-follower driven with a disc cam, 
(a) the pressure angle should be larger during rise than that during return for 
ease of transmitting motion 
(b) the pressure angle should be smaller during rise than that during return for 
ease of transmitting motion 
(c) the pressure angle should be large during rise as well as during return for 
ease of transmitting motion 
(d) the pressure angle does not affect the ease of transmitting motion 
1.6 The shape of the bending moment diagram for a uniform cantilever beam 
carrying a uniformly distributed load over its length is 
(a) a straight line   (b) a hyperbola 
(c) a ellipse   (d) a parabola 
Page 2


GATE ME - 2001
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 The divergence of vector r xi yj zk = + +
r r r r
is 
(a) i j k + +
r r r
(b) 3 (c) 0 (d) 1 
1.2 Consider the system of equations given below: 
2
2 2 5
x y
x y
+ =
+ =
This system has 
(a) one solution (b) no solution 
(c) infinite solutions (d) four solutions 
1.3 What is the derivative of ( ) at 0? f z x x = =
(a) 1 (b) -1 
(c) 0 (d) Does not exist 
1.4 The Gauss divergence theorem relates certain 
(a) surface integrals to volume integrals 
(b) surface integrals to line integrals 
(c) vector quantities to other vector quantities 
(d) line integrals to volume integrals 
1.5 For a spring-loaded roller-follower driven with a disc cam, 
(a) the pressure angle should be larger during rise than that during return for 
ease of transmitting motion 
(b) the pressure angle should be smaller during rise than that during return for 
ease of transmitting motion 
(c) the pressure angle should be large during rise as well as during return for 
ease of transmitting motion 
(d) the pressure angle does not affect the ease of transmitting motion 
1.6 The shape of the bending moment diagram for a uniform cantilever beam 
carrying a uniformly distributed load over its length is 
(a) a straight line   (b) a hyperbola 
(c) a ellipse   (d) a parabola 
GATE ME - 2001
1.7 In the figure shown, the spring deflects by d 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) 
2
1
2
kx (b) 
2
1
2
kx mgx -
(c) ( )
2 1
2
k x d + (d) 
2
1
2
kx mgx +
1.8 A particle P is projected from the earth surface at latitude 45° with escape 
velocity v=11.19 km/s. the velocity direction makes an angle a with the local 
vertical. The particle will escape the earth’s gravitational field 
(a) only when a = 0 
(b) only when a = 45° 
(c) only when a = 90° 
(d) irrespective of the value of a 
1.9 Bars AB and BC, each of negligible mass, support load P as shown in the figure. 
In this arrangement, 
(a) bar AB is subjected to bending but bar BC is not subjected to bending 
(b) bar AB is not subjected to bending but bar BC is subjected to bending 
(c) neither bar AB nor bar BC is subjected to bending 
(d) both bars AB and BC are subjected to bending 
1.10 The area moment of inertia of a square of size 1 unit about its diagonal is 
(a) 
1
3
(b) 
1
4
(c) 
1
12
(d) 
1
6
k 
d 
m 
A 
B 
x 
Free length 
45° 
a P 
N 
? 
Earth 
C 
A 
B 
P 
Page 3


GATE ME - 2001
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 The divergence of vector r xi yj zk = + +
r r r r
is 
(a) i j k + +
r r r
(b) 3 (c) 0 (d) 1 
1.2 Consider the system of equations given below: 
2
2 2 5
x y
x y
+ =
+ =
This system has 
(a) one solution (b) no solution 
(c) infinite solutions (d) four solutions 
1.3 What is the derivative of ( ) at 0? f z x x = =
(a) 1 (b) -1 
(c) 0 (d) Does not exist 
1.4 The Gauss divergence theorem relates certain 
(a) surface integrals to volume integrals 
(b) surface integrals to line integrals 
(c) vector quantities to other vector quantities 
(d) line integrals to volume integrals 
1.5 For a spring-loaded roller-follower driven with a disc cam, 
(a) the pressure angle should be larger during rise than that during return for 
ease of transmitting motion 
(b) the pressure angle should be smaller during rise than that during return for 
ease of transmitting motion 
(c) the pressure angle should be large during rise as well as during return for 
ease of transmitting motion 
(d) the pressure angle does not affect the ease of transmitting motion 
1.6 The shape of the bending moment diagram for a uniform cantilever beam 
carrying a uniformly distributed load over its length is 
(a) a straight line   (b) a hyperbola 
(c) a ellipse   (d) a parabola 
GATE ME - 2001
1.7 In the figure shown, the spring deflects by d 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) 
2
1
2
kx (b) 
2
1
2
kx mgx -
(c) ( )
2 1
2
k x d + (d) 
2
1
2
kx mgx +
1.8 A particle P is projected from the earth surface at latitude 45° with escape 
velocity v=11.19 km/s. the velocity direction makes an angle a with the local 
vertical. The particle will escape the earth’s gravitational field 
(a) only when a = 0 
(b) only when a = 45° 
(c) only when a = 90° 
(d) irrespective of the value of a 
1.9 Bars AB and BC, each of negligible mass, support load P as shown in the figure. 
In this arrangement, 
(a) bar AB is subjected to bending but bar BC is not subjected to bending 
(b) bar AB is not subjected to bending but bar BC is subjected to bending 
(c) neither bar AB nor bar BC is subjected to bending 
(d) both bars AB and BC are subjected to bending 
1.10 The area moment of inertia of a square of size 1 unit about its diagonal is 
(a) 
1
3
(b) 
1
4
(c) 
1
12
(d) 
1
6
k 
d 
m 
A 
B 
x 
Free length 
45° 
a P 
N 
? 
Earth 
C 
A 
B 
P 
GATE ME - 2001
1.11 Which of the following statement is correct? 
(a) Flywheel reduces speed fluctuations during a cycle for a constant load, but 
flywheel does not control the mean speed of the engine if the load changes. 
(b) Flywheel does not reduce speed fluctuation during a cycle for a constant 
load, but flywheel does not control the mean speed of the engine if the load 
changes. 
(c) Governor controls speed fluctuations during a cycle for a constant load, but 
governor does not control the mean speed of the engine if the load changes. 
(d) Governor controls speed fluctuations during a cycle for a constant load, and 
governor also control the mean speed of the engine if the load changes. 
1.12  The SI unit of kinematic viscosity (?) is 
(a) m
2
/sec (b) kg/(m-sec) (c) m/sec
2
 (d) m
3
/sec
2
1.13 A static fluid can have 
(a) non-zero normal and shear stress 
(b) negative normal stress and zero shear stress 
(c) positive normal stress and zero shear stress  
(d) zero normal stress and non-zero shear stress 
1.14 A gas having a negative Joule-Thompson coefficient (µ < 0), when throttled, will 
(a) become cooler   (b) become warmer 
(c) remain at the same temperature 
(d) either be cooler or warmer depending on the type of gas 
1.15 Lumped heat transfer analysis of a solid object suddenly exposed to a fluid 
medium at a different temperature is valid when  
(a) Biot number < 0.1  (b) Biot number > 0.1  
(c) Fourier number < 0.1  (d) Fourier number > 0.1 
1.16 The Rateau turbine belongs to the category of 
(a) pressure compounded turbine (b) reaction turbine 
(c) velocity compounded turbine (d) radial flow turbine 
1.17 For the circular tube of equal length and diameter 
shown below, the view factor F
13
 is 0.17. the view factor 
F
12
 in this case will be 
(a) 0.17 
(b) 0.21 
(c) 0.79 
(d) 0.83 
A 2 
A 1 
A 3 
D 
L=D 
Page 4


GATE ME - 2001
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 The divergence of vector r xi yj zk = + +
r r r r
is 
(a) i j k + +
r r r
(b) 3 (c) 0 (d) 1 
1.2 Consider the system of equations given below: 
2
2 2 5
x y
x y
+ =
+ =
This system has 
(a) one solution (b) no solution 
(c) infinite solutions (d) four solutions 
1.3 What is the derivative of ( ) at 0? f z x x = =
(a) 1 (b) -1 
(c) 0 (d) Does not exist 
1.4 The Gauss divergence theorem relates certain 
(a) surface integrals to volume integrals 
(b) surface integrals to line integrals 
(c) vector quantities to other vector quantities 
(d) line integrals to volume integrals 
1.5 For a spring-loaded roller-follower driven with a disc cam, 
(a) the pressure angle should be larger during rise than that during return for 
ease of transmitting motion 
(b) the pressure angle should be smaller during rise than that during return for 
ease of transmitting motion 
(c) the pressure angle should be large during rise as well as during return for 
ease of transmitting motion 
(d) the pressure angle does not affect the ease of transmitting motion 
1.6 The shape of the bending moment diagram for a uniform cantilever beam 
carrying a uniformly distributed load over its length is 
(a) a straight line   (b) a hyperbola 
(c) a ellipse   (d) a parabola 
GATE ME - 2001
1.7 In the figure shown, the spring deflects by d 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) 
2
1
2
kx (b) 
2
1
2
kx mgx -
(c) ( )
2 1
2
k x d + (d) 
2
1
2
kx mgx +
1.8 A particle P is projected from the earth surface at latitude 45° with escape 
velocity v=11.19 km/s. the velocity direction makes an angle a with the local 
vertical. The particle will escape the earth’s gravitational field 
(a) only when a = 0 
(b) only when a = 45° 
(c) only when a = 90° 
(d) irrespective of the value of a 
1.9 Bars AB and BC, each of negligible mass, support load P as shown in the figure. 
In this arrangement, 
(a) bar AB is subjected to bending but bar BC is not subjected to bending 
(b) bar AB is not subjected to bending but bar BC is subjected to bending 
(c) neither bar AB nor bar BC is subjected to bending 
(d) both bars AB and BC are subjected to bending 
1.10 The area moment of inertia of a square of size 1 unit about its diagonal is 
(a) 
1
3
(b) 
1
4
(c) 
1
12
(d) 
1
6
k 
d 
m 
A 
B 
x 
Free length 
45° 
a P 
N 
? 
Earth 
C 
A 
B 
P 
GATE ME - 2001
1.11 Which of the following statement is correct? 
(a) Flywheel reduces speed fluctuations during a cycle for a constant load, but 
flywheel does not control the mean speed of the engine if the load changes. 
(b) Flywheel does not reduce speed fluctuation during a cycle for a constant 
load, but flywheel does not control the mean speed of the engine if the load 
changes. 
(c) Governor controls speed fluctuations during a cycle for a constant load, but 
governor does not control the mean speed of the engine if the load changes. 
(d) Governor controls speed fluctuations during a cycle for a constant load, and 
governor also control the mean speed of the engine if the load changes. 
1.12  The SI unit of kinematic viscosity (?) is 
(a) m
2
/sec (b) kg/(m-sec) (c) m/sec
2
 (d) m
3
/sec
2
1.13 A static fluid can have 
(a) non-zero normal and shear stress 
(b) negative normal stress and zero shear stress 
(c) positive normal stress and zero shear stress  
(d) zero normal stress and non-zero shear stress 
1.14 A gas having a negative Joule-Thompson coefficient (µ < 0), when throttled, will 
(a) become cooler   (b) become warmer 
(c) remain at the same temperature 
(d) either be cooler or warmer depending on the type of gas 
1.15 Lumped heat transfer analysis of a solid object suddenly exposed to a fluid 
medium at a different temperature is valid when  
(a) Biot number < 0.1  (b) Biot number > 0.1  
(c) Fourier number < 0.1  (d) Fourier number > 0.1 
1.16 The Rateau turbine belongs to the category of 
(a) pressure compounded turbine (b) reaction turbine 
(c) velocity compounded turbine (d) radial flow turbine 
1.17 For the circular tube of equal length and diameter 
shown below, the view factor F
13
 is 0.17. the view factor 
F
12
 in this case will be 
(a) 0.17 
(b) 0.21 
(c) 0.79 
(d) 0.83 
A 2 
A 1 
A 3 
D 
L=D 
GATE ME - 2001
1.18 In descending order of magnitude, the thermal conductivity of (a) pure iron, (b) 
liquid water, (c) saturated water vapour and (d) aluminum can be arranged as 
(a) a b c d (b) b c a d (c) d a b c (d) d c b a 
1.19. Shrinkage allowance on pattern is provided to compensate for shrinkage when 
(a) the temperature of liquid metal drops from pouring to freezing temperature
(b) the metal changes from liquid to solid state at freezing temperature 
(c) the temperature of solid phase drops from freezing to room temperature  
(d) the temperature of metal drops from pouring to room temperature 
1.20. The cutting force in punching and blanking operations mainly depends on 
(a) the modulus of elasticity of metal (b) the shear strength of metal 
(c) the bulk modulus of metal (d) the yield strength of metal 
1.21. In ECM, the material removal is due to 
(a) corrosion (b) erosion 
(c) fusion (d) ion displacement 
1.22. Two plates of the same metal having equal thickness are to be butt welded with 
electric arc. When the plate thickness changes, welding is achieved by  
(a) adjusting the current  (b) adjusting the duration of current 
(c) changing the electrode size (d) changing the electrode coating 
1.23. Allowance in limits and fits refers to 
(a) maximum clearance between shaft and hole  
(b) minimum clearance between shaft and hole  
(c) difference between maximum and minimum size of hole 
(d) difference between maximum and minimum size of shaft 
1.24. Production flow analysis (PFA) is a method of identifying part families that uses 
data from 
(a) engineering drawings  (b) production schedule 
(c) bill of materials   (d) route sheets 
1.25 When using a simple moving average to forecast demand, one would 
(a) give equal weight to all demand data 
(b) assign more weight to the recent demand data 
(c) include new demand data in the average without discarding the earlier data 
(d) include new demand data in the average after discarding some of the earlier 
demand data 
Page 5


GATE ME - 2001
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 The divergence of vector r xi yj zk = + +
r r r r
is 
(a) i j k + +
r r r
(b) 3 (c) 0 (d) 1 
1.2 Consider the system of equations given below: 
2
2 2 5
x y
x y
+ =
+ =
This system has 
(a) one solution (b) no solution 
(c) infinite solutions (d) four solutions 
1.3 What is the derivative of ( ) at 0? f z x x = =
(a) 1 (b) -1 
(c) 0 (d) Does not exist 
1.4 The Gauss divergence theorem relates certain 
(a) surface integrals to volume integrals 
(b) surface integrals to line integrals 
(c) vector quantities to other vector quantities 
(d) line integrals to volume integrals 
1.5 For a spring-loaded roller-follower driven with a disc cam, 
(a) the pressure angle should be larger during rise than that during return for 
ease of transmitting motion 
(b) the pressure angle should be smaller during rise than that during return for 
ease of transmitting motion 
(c) the pressure angle should be large during rise as well as during return for 
ease of transmitting motion 
(d) the pressure angle does not affect the ease of transmitting motion 
1.6 The shape of the bending moment diagram for a uniform cantilever beam 
carrying a uniformly distributed load over its length is 
(a) a straight line   (b) a hyperbola 
(c) a ellipse   (d) a parabola 
GATE ME - 2001
1.7 In the figure shown, the spring deflects by d 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) 
2
1
2
kx (b) 
2
1
2
kx mgx -
(c) ( )
2 1
2
k x d + (d) 
2
1
2
kx mgx +
1.8 A particle P is projected from the earth surface at latitude 45° with escape 
velocity v=11.19 km/s. the velocity direction makes an angle a with the local 
vertical. The particle will escape the earth’s gravitational field 
(a) only when a = 0 
(b) only when a = 45° 
(c) only when a = 90° 
(d) irrespective of the value of a 
1.9 Bars AB and BC, each of negligible mass, support load P as shown in the figure. 
In this arrangement, 
(a) bar AB is subjected to bending but bar BC is not subjected to bending 
(b) bar AB is not subjected to bending but bar BC is subjected to bending 
(c) neither bar AB nor bar BC is subjected to bending 
(d) both bars AB and BC are subjected to bending 
1.10 The area moment of inertia of a square of size 1 unit about its diagonal is 
(a) 
1
3
(b) 
1
4
(c) 
1
12
(d) 
1
6
k 
d 
m 
A 
B 
x 
Free length 
45° 
a P 
N 
? 
Earth 
C 
A 
B 
P 
GATE ME - 2001
1.11 Which of the following statement is correct? 
(a) Flywheel reduces speed fluctuations during a cycle for a constant load, but 
flywheel does not control the mean speed of the engine if the load changes. 
(b) Flywheel does not reduce speed fluctuation during a cycle for a constant 
load, but flywheel does not control the mean speed of the engine if the load 
changes. 
(c) Governor controls speed fluctuations during a cycle for a constant load, but 
governor does not control the mean speed of the engine if the load changes. 
(d) Governor controls speed fluctuations during a cycle for a constant load, and 
governor also control the mean speed of the engine if the load changes. 
1.12  The SI unit of kinematic viscosity (?) is 
(a) m
2
/sec (b) kg/(m-sec) (c) m/sec
2
 (d) m
3
/sec
2
1.13 A static fluid can have 
(a) non-zero normal and shear stress 
(b) negative normal stress and zero shear stress 
(c) positive normal stress and zero shear stress  
(d) zero normal stress and non-zero shear stress 
1.14 A gas having a negative Joule-Thompson coefficient (µ < 0), when throttled, will 
(a) become cooler   (b) become warmer 
(c) remain at the same temperature 
(d) either be cooler or warmer depending on the type of gas 
1.15 Lumped heat transfer analysis of a solid object suddenly exposed to a fluid 
medium at a different temperature is valid when  
(a) Biot number < 0.1  (b) Biot number > 0.1  
(c) Fourier number < 0.1  (d) Fourier number > 0.1 
1.16 The Rateau turbine belongs to the category of 
(a) pressure compounded turbine (b) reaction turbine 
(c) velocity compounded turbine (d) radial flow turbine 
1.17 For the circular tube of equal length and diameter 
shown below, the view factor F
13
 is 0.17. the view factor 
F
12
 in this case will be 
(a) 0.17 
(b) 0.21 
(c) 0.79 
(d) 0.83 
A 2 
A 1 
A 3 
D 
L=D 
GATE ME - 2001
1.18 In descending order of magnitude, the thermal conductivity of (a) pure iron, (b) 
liquid water, (c) saturated water vapour and (d) aluminum can be arranged as 
(a) a b c d (b) b c a d (c) d a b c (d) d c b a 
1.19. Shrinkage allowance on pattern is provided to compensate for shrinkage when 
(a) the temperature of liquid metal drops from pouring to freezing temperature
(b) the metal changes from liquid to solid state at freezing temperature 
(c) the temperature of solid phase drops from freezing to room temperature  
(d) the temperature of metal drops from pouring to room temperature 
1.20. The cutting force in punching and blanking operations mainly depends on 
(a) the modulus of elasticity of metal (b) the shear strength of metal 
(c) the bulk modulus of metal (d) the yield strength of metal 
1.21. In ECM, the material removal is due to 
(a) corrosion (b) erosion 
(c) fusion (d) ion displacement 
1.22. Two plates of the same metal having equal thickness are to be butt welded with 
electric arc. When the plate thickness changes, welding is achieved by  
(a) adjusting the current  (b) adjusting the duration of current 
(c) changing the electrode size (d) changing the electrode coating 
1.23. Allowance in limits and fits refers to 
(a) maximum clearance between shaft and hole  
(b) minimum clearance between shaft and hole  
(c) difference between maximum and minimum size of hole 
(d) difference between maximum and minimum size of shaft 
1.24. Production flow analysis (PFA) is a method of identifying part families that uses 
data from 
(a) engineering drawings  (b) production schedule 
(c) bill of materials   (d) route sheets 
1.25 When using a simple moving average to forecast demand, one would 
(a) give equal weight to all demand data 
(b) assign more weight to the recent demand data 
(c) include new demand data in the average without discarding the earlier data 
(d) include new demand data in the average after discarding some of the earlier 
demand data 
GATE ME - 2001
Sun 20T 
arm 
ring 80T 
Planet 
30T 
2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
2.1 The minimum point of the function ( )
( )
3
3 f x x x = - is at
(a) x = 1 (b) x = -1 (c) x = 0 (d) 
1
3
x =
2.2. The rank of a 3 × 3 matrix C ( = AB), found by multiplying a non-zero column 
matrix A of size 3 × 1 and a non-zero row matrix B of size 1 × 3, is 
(a) 0 (b) 1 (c) 2 (d) 3  
2.3. An unbiased coin is tossed three times. The probability that the head turns up in 
exactly two cases is 
(a) 
1
9
(b) 
1
8
(c) 
2
3
(d) 
3
8
2.4. Two helical tensile springs of the same material and also having identical mean 
coil diameter and weight, have wire diameters d and .
2
d
 The ratio of their 
stiffness is 
(a) 1 (b) 4 (c) 64 (d) 128 
2.5. The maximum principal stress for the stress state shown in the figure is 
(a) s (b) 2s (c) 3s (d) 1.5s 
2.6. The sun gear in the figure is driven clockwise at 100 rpm. The ring gear is held 
stationary. For the number of teeth shown on the gears, the arm rotates at 
(a) 0 rpm (b) 20 rpm (c) 33.33 rpm (d) 66.67 rpm 
s 
s 
s 
s 
s 
s