Hollow shafts are stronger than solid shafts having same weight because

the natural frequency of hollow shaft is less than that of solid shaft.

the stiffness of hollow shaft is less than that of solid shaft.

the strength of hollow shaft is more than that of solid shaft.

the natural frequency of hollow shaft is less than that of solid shaft.

in hollow shafts, material is not spread at large radius.

A circular shaft is subjected to torque. The torsional rigidity is defined as:

ratio of torque and polar moment of inertia

product of polar moment of inertia and modulus of rigidity

ratio of torque and polar moment of inertia

sum of polar moment of inertia and modulus of rigidity

A hollow shaft of the same cross-section area and material as that of a solid shaft transmits:

Cannot be predicted without more data

For the two shafts connected in parallel

Torsional stiffness of each shaft is the same

Torque in each shaft is the same

Shear stress in shaft is the same

Angle of twist of each shaft is the same

Torsional stiffness of each shaft is the same

Pick up the incorrect statement from the following:The torsional resistance of a shaft is directly proportional to

reciprocal of the length of the shaft

moment of inertia of the shaft section

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist θ at the free end is

\({\left( {\frac{{16TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)

\({\left( {\frac{{32TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)

\({\left( {\frac{{18TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)

\({\left( {\frac{{16TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)

\({\left( {\frac{{2TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)

54 + Mcqs in Torsion Of Shaft in Civil Engineering Page 1 McqOptions

1.	A propeller shaft is required to transmit 45 kW power at 500 r.p.m. It is hollow shaft having inside diameter 0.6 times the outside diameter. It is made of plain carbon steel and the permissible shear stress is 84 N/mm2. The inner and outer diameters of the shaft are nearly
A.	21.7 mm and 39.1 mm
B.	23.5 mm and 39.1 mm
C.	21.7 mm and 32.2 mm
D.	23.5 mm and 32.2 mm
Answer» C. 21.7 mm and 32.2 mm

Discussion

2.	A shaft rotating at 150 rpm is subjected to a torque of 1500 N.m. Horse power transmitted by the shaft is
A.	π2
B.	π
C.	10π
D.	1/10π
Answer» D. 1/10π

Discussion

3.	A circular shaft of diameter d and length l is subjected to a torque T and a bending moment M. The ratio of maximum shear stress to bending stress is:
A.	\(\frac{{2T}}{M}\)
B.	\(\frac{T}{{2M}}\)
C.	\(\frac{T}{M}\)
D.	\(\frac{T}{{4M}}\)
Answer» C. \(\frac{T}{M}\)

Discussion

4.	Hollow shafts are stronger than solid shafts having same weight because
A.	the stiffness of hollow shaft is less than that of solid shaft.
B.	the strength of hollow shaft is more than that of solid shaft.
C.	the natural frequency of hollow shaft is less than that of solid shaft.
D.	in hollow shafts, material is not spread at large radius.
Answer» C. the natural frequency of hollow shaft is less than that of solid shaft.

Discussion

5.	Power transmitted by a shaft is given by expression _______ in kilowatts
A.	\(\frac{2\pi NT}{60}\)
B.	\(\frac{60}{2\pi NT}\)
C.	\(\frac{3\pi NT}{60}\)
D.	\(\frac{60}{3\pi NT}\)
Answer» B. \(\frac{60}{2\pi NT}\)

Discussion

6.	A solid circular shaft needs to be designed to transmit a torque of 55 N m. if the allowable shear stress of the material is 280 N/mm2, find the diameter (in mm) of the shaft required to transmit the torque. (Assume, π = 22/7)
A.	5.62
B.	10
C.	31.62
D.	25
Answer» C. 31.62

Discussion

7.	A circular shaft subjected to torsion undergoes a twist of 1° in length of 120 cm. If the maximum shear stress induced is limited to 1000 kg/cm2 and if modulus of rigidity G = 0.8 × 106 kg/cm2, then the radius of the shaft (in cm) should be
A.	π/18
B.	18/π
C.	π/27
D.	27/π
Answer» E.

Discussion

8.	For the same cross sectional area (or weight), ________ shafts have higher strength and rigidity than _______ shafts.
A.	solid, hollow
B.	hollow, solid
C.	Both are equal
D.	None of these
Answer» C. Both are equal

Discussion

9.	A bar of circular cross-section of diameter D is subject to a torque T at B as shown in figure given below.What is the angle of twist at A with respect to B ?
A.	Same as that at B
B.	Zero
C.	Twice as that at B
D.	Half as that at B
Answer» C. Twice as that at B

Discussion

10.	A solid circular beam with a radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The shear stress component τxy at point ‘M’ in cross-section of the beam at a distance of 1 m from the fixed end is
A.	0.0 MPa
B.	0.51 MPa
C.	0.815 MPa
D.	2.0 MPa
Answer» B. 0.51 MPa

Discussion

11.	A circular shaft is subjected to torque. The torsional rigidity is defined as:
A.	product of polar moment of inertia and modulus of rigidity
B.	ratio of torque and polar moment of inertia
C.	product of torque and length
D.	sum of polar moment of inertia and modulus of rigidity
Answer» B. ratio of torque and polar moment of inertia

Discussion

12.	Maximum shear stress in a solid shaft of diameter D and length L twisted through an angle θ is τ. A hollow shaft of the same material and length having outside and inside diameters of D and D/2 respectively is also twisted through the same angle of twist θ. The value of maximum shear stress in the hollow shaft will be
A.	\(\frac{{16}}{{15}}\tau \)
B.	\(\frac{{8}}{{7}}\tau \)
C.	\(\frac{{4}}{{3}}\tau \)
D.	\(\tau\)
Answer» E.

Discussion

13.	If the diameter of the shaft is 'D', and the shear stress is τ, then how much torque will be transmitted by the shaft?
A.	(π / 8)τD3
B.	(π / 16)τD3
C.	(π / 64)τD3
D.	(π / 32)τD3
Answer» C. (π / 64)τD3

Discussion

14.	In case of a circular section the section modulus is given as
A.	πd2/16
B.	πd3/16
C.	πd3/32
D.	πd3/64
Answer» D. πd3/64

Discussion

15.	A torsional system with discs of moment of inertia I1 and I2 are shown in figure, which are gear driven. The ratio of speed of shaft B to shaft A is G. The equivalent moment of inertia of disc on shaft B at the speed of shaft ‘A’ is equal to
A.	GI2
B.	G2I2
C.	I2/G
D.	I2/G2
Answer» C. I2/G

Discussion

16.	A solid shaft A of dimeter D and length L is subjected to a torque T; another shaft B of the same material and of the same length, but half the diameter, is also subjected to the same torque T. the ratio between the angles of twist of shaft B to that of shaft A is
A.	32
B.	16
C.	8
D.	4
Answer» C. 8

Discussion

17.	A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is
A.	2
B.	1
C.	0.5
D.	0
Answer» C. 0.5

Discussion

18.	A structural system consists of two springs, each of stiffness k, in parallel in-turn connected to third spring of same stiffness in series. A mass m is connected at the one end of the system and other end is fixed. What shall be the natural frequency of the system?
A.	\(\sqrt {\frac{k}{m}} \)
B.	\(\sqrt {\frac{{3k}}{m}} \)
C.	\(\sqrt {\frac{{3k}}{{2m}}} \)
D.	\(\sqrt {\frac{{2k}}{{3m}}} \)
Answer» E.

Discussion

19.	A solid shaft of 2 m diameter is used to transmit torque. The maximum shear stress induced to the shaft is 100 N/m2 . Determine the maximum torque transmitted by the shaft.
A.	146 N-m
B.	188 N-m
C.	165 N-m
D.	157 N-m
Answer» E.

Discussion

20.	A hollow shaft of the same cross-section area and material as that of a solid shaft transmits:
A.	Same torque
B.	Lesser torque
C.	More torque
D.	Cannot be predicted without more data
Answer» D. Cannot be predicted without more data

Discussion

21.	A solid circular shaft needs to be designed to transmit a torque of 50 Nm. If the allowable shear stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is
A.	8
B.	16
C.	24
D.	32
Answer» C. 24

Discussion

22.	For the two shafts connected in parallel
A.	Torque in each shaft is the same
B.	Shear stress in shaft is the same
C.	Angle of twist of each shaft is the same
D.	Torsional stiffness of each shaft is the same
Answer» D. Torsional stiffness of each shaft is the same

Discussion

23.	A rectangular bar has been subjected to torsion. The maximum shear stress will occur _______.
A.	At the centre
B.	At the corner
C.	At the middle of longer side
D.	Along the diagonal
Answer» D. Along the diagonal

Discussion

24.	If two shafts of the same length, one of which is hollow, transmit equal torques and have equal maximum stress, then they should have equal
A.	Polar moment of inertia
B.	Polar modulus of section
C.	Diameter
D.	Angle of twist
Answer» C. Diameter

Discussion

25.	A shaft can safely transmit 90 kW while rotating at a given speed. If this shaft is replaced by a shaft of diameter double of the previous one and rotated at half the speed of the previous, the power that can be transmitted by the new shaft is:
A.	90 kW
B.	180 kW
C.	360 kW
D.	720 kW
Answer» D. 720 kW

Discussion

26.	Maximum shear stress developed on the surface of solid circular shaft under pure torsion is 400 MPa. If shaft diameter is double, then the maximum shear stress developed corresponding to the same torque will be
A.	200 MPa
B.	1600 MPa
C.	100 MPa
D.	50 MPa
Answer» E.

Discussion

27.	A torsion member is fabricated from two concentric thin tubes. At the ends, the tubes are welded to rigid discs so that both the tubes are twisted as a unit. The radius of the outer tube is 2r and that of the inner tube is r. If the shear stresses developed in the outer tube is 'τ', then the shear stress in the inner tube will be ________.
A.	τ
B.	0.25 τ
C.	0.75 τ
D.	0.5 τ
Answer» E.

Discussion

28.	A solid shaft of diameter ‘D’ carries a twisting moment that develops maximum shear stress τ. If this shaft is replaced by a hollow one of outside diameter D and inside diameter D/2, then the maximum shear stress will be
A.	1.067τ
B.	1.145τ
C.	1.335τ
D.	2τ
Answer» B. 1.145τ

Discussion

29.	A solid shaft can resist a bending moment of 3 kNm and a twisting moment of 4 kNm together, then the maximum torque that can be applied is _____.
A.	7.0 kNm
B.	3.5 kNm
C.	4.5 kNm
D.	5.0 kNm
Answer» E.

Discussion

30.	A hollow shaft do = 2di where do and di are the outer and inner diameters respectively needs to transmit 20kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, dO is
A.	11.29 mm
B.	22.58 mm
C.	33.08 mm
D.	45.16 mm
Answer» C. 33.08 mm

Discussion

31.	If a shaft is required to transmit twice the power at twice the speed for which it is designed, its diameter must
A.	increase two times
B.	reduce two times
C.	remain same
D.	increase three times
Answer» D. increase three times

Discussion

32.	A shaft of 20 mm diameter and length 1 m is subjected to a twisting moment, due to which shear strain on the surface of the shaft is 0.001. The angular twist in the shaft is
A.	0.10 radian
B.	0.01 radian
C.	0.05 radian
D.	0.50 radian
Answer» B. 0.01 radian

Discussion

33.	If the strain energy stored per unit volume in a hollow shaft subjected to a pure torque when t attains maximum shear stress fs is (17 fs2)/(64G), the ratio of the inner diameter to outer diameter is
A.	1/2
B.	1/3
C.	1/4
D.	1/5
Answer» D. 1/5

Discussion

34.	A circular shaft is subjected to a twisting moment T and bending moment M. The ratio of Maximum bending stress to Maximum shear stress is given by:
A.	2M/T
B.	M/T
C.	2T/M
D.	M/2T
Answer» B. M/T

Discussion

35.	A metal shaft of solid circular section rotates as 160 rpm and is subjected to a torque of 1500 Nm. What is the power, in kW, transmitted by the shaft?
A.	32 π
B.	16 π
C.	12 π
D.	8 π
Answer» E.

Discussion

36.	Pick up the incorrect statement from the following:The torsional resistance of a shaft is directly proportional to
A.	modulus of rigidity
B.	angle of twist
C.	reciprocal of the length of the shaft
D.	moment of inertia of the shaft section
Answer» E.

Discussion

37.	At the free end of a shaft, angle of twist is: ______.
A.	Zero
B.	Low
C.	Moderate
D.	Maximum
Answer» E.

Discussion

38.	If a close coiled helical spring absorbs 30 N-mm of energy while extending by 5 mm, its stiffness will be ______.
A.	2 N/mm
B.	4 N/mm
C.	2.4 N/mm
D.	10 N/mm
Answer» D. 10 N/mm

Discussion

39.	A steel spindle transmits 4 kW at 800 r.p.m. The angular deflection should not exceed 0.25°/m length of the spindle. If the modulus of rigidity for the material of the spindle is 84 GPa, the diameter of the spindle will be
A.	46 mm
B.	42 mm
C.	38 mm
D.	34 mm
Answer» E.

Discussion

40.	Power transmitted by a shaft in watts is given by the expression
A.	\(P = \frac{{60}}{{2\pi NT}}\)
B.	\(P = \frac{{2\pi NT}}{{60}}\)
C.	\(P = \frac{{4\pi NT}}{{60}}\)
D.	\(P = \frac{{60}}{{4\pi NT}}\)
Answer» C. \(P = \frac{{4\pi NT}}{{60}}\)

Discussion

41.	A stepped steel shaft is subjected to a clockwise torque of 10 Nm at its free end. Shear modulus of steel is 80 GPa. The strain energy stored in the shaft is
A.	1.73 Nmm
B.	2.52 Nmm
C.	3.46 Nmm
D.	4.12 Nmm
Answer» B. 2.52 Nmm

Discussion

42.	Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corresponding to the same torque will be
A.	120 MPa
B.	60 MPa
C.	30 MPa
D.	15 MPa
Answer» D. 15 MPa

Discussion

43.	A hollow steel shaft has outside diameter d and inside diameter \(\frac{d}{2}\). The value of d for the shaft, if it has to transmit 200hp at 105 rpm with a working shear stress of 420 kg/cm2, is
A.	5.6 cm
B.	2.6 cm
C.	12.1 cm
D.	15.5 cm
Answer» D. 15.5 cm

Discussion

44.	If a body is transmitting torque T N - m at N rpm, then power (in Watts) transmitted will be:-
A.	TN
B.	TN/75
C.	TN/4500
D.	2πNT/60
Answer» E.

Discussion

45.	A hollow circular shaft of outside diameter 100 mm and an internal diameter of 90 mm is subjected to a torque T = 3π kNm. Polar moment of inertia of circular section is: π × 10-6 m4. Maximum shear stress on the shaft is given by:
A.	100 MPa
B.	125 MPa
C.	150 MPa
D.	175 MPa
Answer» D. 175 MPa

Discussion

46.	In a rectangular shaft subjected to torsion, the maximum shear occurs at
A.	Centre
B.	Corners
C.	Middle of smaller side
D.	Middle of larger side
Answer» E.

Discussion

47.	A shaft of length L having torsional rigidity GJ is subjected to a torque the corresponding stiffness shall be:
A.	\(\frac{{TJ}}{L}\)
B.	\(\frac{{GJ}}{L}\)
C.	\(\frac{{TG}}{L}\)
D.	\(\frac{{TJ}}{{GL}}\)
Answer» C. \(\frac{{TG}}{L}\)

Discussion

48.	If the horse power of a shaft subjected to torque alone is doubled, horse power can be increased
A.	8 times
B.	4 times
C.	16 times
D.	2 times
Answer» E.

Discussion

49.	A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist θ at the free end is
A.	\({\left( {\frac{{32TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)
B.	\({\left( {\frac{{18TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)
C.	\({\left( {\frac{{16TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)
D.	\({\left( {\frac{{2TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)
Answer» C. \({\left( {\frac{{16TL}}{{\pi \theta G}}} \right)^{\frac{1}{4}}}\)

Discussion

50.	A circular shaft rotates at 200 rpm and is subject to a torque of 1500 Nm. The power transmitted would be
A.	10 π kW
B.	15 π kW
C.	20 π kW
D.	30 π kW
Answer» B. 15 π kW

Discussion

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