Torsion | Strength of Materials | GATE MCQs (solved)

GATE ME solved Questions on Torsion (Strength of Materials)

Question #1

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r3 > r1 and r4 > r2 and that the areas of the cross-sections are the same. J1 and J2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J2/J1 is

[GATE 2016 Set 1, 1 mark]


(A) > 1

(B) < 0.5

(C) =1

(D) between 0.5 and 1

Question #2

A rigid horizontal rod of length 2L is fixed to a circular cylinder of radius R as shown in the figure. Vertical forces of magnitude P are applied at the two ends as shown in the figure. The shear modulus for the cylinder is G and the Young’s modulus is E.

[GATE 2016 Set 2, 2 marks]


The vertical deflection at point A is

(A) $PL^3$ / $\pi$ $R^4G$

(B)   $PL^3$ / $\pi$ $R^4E$

(C) $2PL^3$ / $\pi$ $R^4E$

(D) $4PL^3$ / $\pi$ $R^4G$

Question #3

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, \LARGE \tauS is the twist and \LARGE \tau S is the maximum shear stress in the solid shaft, whereas \LARGE \tauH is the twist and \LARGE \tauH is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

[GATE 2016 Set 3, 2 marks]

(A) $\theta$ s  = $\theta$ H and $\tau$ s = $\tau$ H
(B)$\theta$ S > $\theta$ H and $\tau$ S > $\tau$ H
(C)$\theta$S < $\theta$H and $\tau$S < $\tau$H
(D)$\theta$S = $\theta$H and $\tau$S <$\tau$H

Question #4

Consider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G = 77 GPa. The angle of twist at C (in degrees) is __________

[GATE 2015 Set 1, 1 mark]

Question #5

A rope-brake dynamometer attached to the crankshaft of an I.C. engine measures a brake power of 10 kW when the speed of rotation of the shaft is 400 rad/s. The shaft torque (in N-m) sensed by the dynamometer is ___________

[GATE 2015 Set 2, 1 mark]

Question #6

A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is 1°. The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The outside diameter (in mm) of the shaft is__________

[GATE 2015 Set 2, 2 marks]

Question #7

Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear stresses developed in the two shafts are $\tau$  and $\tau$  . If R1/ R2=2 , then $\frac{\tau_{1}}{\tau_{2}}$is _______

[GATE 2014 Set 3, 1 mark]


Question #8

A solid circular shaft needs to be designed to transmit a torque of 50 N.m. 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


(B) 16

(C) 24

(D) 32

[GATE 2012, 2 marks]

Question #9

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 diameter to produce an angular twist $\theta$ at the free end is

GATE torsion question

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

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

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

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

[GATE 2011, 2 marks]


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Practice other topics from Strength of Materials:

Stress and strain



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