Engineering Sciences
GATE XE year:2023 PYQs
Build your understanding with focused practice from past exam papers.
Questions 81–90 of 175. Imported answers require independent review unless marked reviewed.
Question 81
Open questionXE-DNAT2 marksNeeds review
A steel ball of mass m = 10 kg is suspended from the ceiling of a moving carriage by two inextensible strings making 60° with the horizontal as shown. The carriage has an acceleration a such that the tension in the string on the right is double the tension in the string on the left. Take the acceleration due to gravity (g) as 10 m/s
. The acceleration a (in m/s
) is_____(rounded off to one decimal place). 
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Open questionXE-DNAT2 marksNeeds review
A block of mass m = 10 kg is lying on an inclined plane PQ. The mass is restrained from sliding down the inclined plane by a force F. The coefficient of friction between the block and the inclined plane is 0.3. Take the acceleration due to gravity as 10 m/s
. The smallest force F (in N) required to prevent the block from sliding down is_____(rounded off to one decimal place). 
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A spherical rigid ball of mass 10 kg is moving with a speed of 2 m/s in the direction shown. The ball collides with a rigid frictionless wall and rebounds at an angle α with a speed of v, as shown. The coefficient of restitution is 0.9. The angle α (in degrees) is_____(rounded off to one decimal place).
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 84
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A thin steel plate is loaded in the x-y plane as shown in the figure. Take the Poisson’s ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200 GPa. The strain along the z-direction is
. The value of
(in MPa) is_____(rounded off to one decimal place). 
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A composite rod made of steel and copper is fixed immovably at its ends as shown in the figure. The length of each portion of the rod is 1 m as shown. The cross-section of both portions are the same. The modulus of elasticity of steel and copper are 200 GPa and 100 GPa, respectively. The coefficients of thermal expansion of steel and copper are 12 × 10
/°C and 18 × 10
/°C, respectively. The composite rod is initially stress free. Then, the temperature of the composite rod is increased by 100 °C. The magnitude of axial stress (in MPa) developed in the steel rod is_____(rounded off to one decimal place). 
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Open questionXE-DNAT2 marksNeeds review
A slender uniform elastic rod of length 1 m and of solid circular cross-section of diameter 50 mm is originally straight. It is then loaded by equal and opposite end moments as indicated in the figure. The resulting lateral displacement of the mid-point of the rod is 10 mm (displacements are exaggerated in the figure). The maximum longitudinal strain in the rod is p × 10
, where p is_____(rounded off to one decimal place). 
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Open questionXE-DNAT2 marksNeeds review
Consider a solid cylindrical shaft and a hollow cylindrical shaft. Both shafts are axisymmetric and elastic, and have the same cross-sectional area. The hollow shaft has an outside diameter of 150 mm and an inside diameter of 120 mm. When both the shafts are twisted by the same twisting moment, the ratio of maximum shear stress developed in the hollow shaft (
) to maximum shear stress developed in the solid shaft (
) will be_____(rounded off to three decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 88
Open questionXE-EMCQ1 markNeeds review
A The number of properties required to fix the state of a system is given by ‘state postulate’. R The state of a simple compressible system is completely specified by two independent, intensive properties. About the statements A and R applied to a single-phase system,
Your answerChoose one option.
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Which of the following is an extensive property of a system?
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Open questionXE-EMCQ1 markNeeds review
A tank of volume V contains homogeneous mixture of two ideal gases, A and B at a temperature T and a pressure P. The mixture contains n_A moles of gas A and n_B moles of gas B. If P_A and P_B are the partial pressures of gas A and gas B, respectively, then
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