GATE XE Properties and Applications of Materials PYQs & Answers — Page 7

Questions 61–70 of 79. Imported answers require independent review unless marked reviewed.

The number of vibrational degrees of freedom for a non-linear triatomic molecule are

Your answerChoose one option.

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For a two-dimensional solid, the variation of lattice specific heat as a function of temperature T (in K, at low temperatures) is given as:

, where b is a constant. The value of n is __________.

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An intrinsic semiconductor has conduction electron concentration, n = 10¹² cm⁻³. The mobility of both electrons and holes are identical = 4 × 10⁴ cm² V⁻¹ s⁻¹. If a voltage of 100 V is applied on two parallel end faces of the cube (edge length 1 cm) through Ohmic contacts, the current through the cube would be (in mA) (Given: charge of electron = 1.6 × 10⁻¹⁹ C)

Your answerChoose one option.

640

1280

600

1280

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An infinite plate with a through-thickness crack of length 2 mm is subjected to a tensile stress (as shown in the figure). Assuming the plate to be linear elastic, the fracture stress is __________ MPa (round off to the nearest whole number)

(Given: Fracture toughness,

)

Diagram for Engineering Sciences question 13

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A unidirectionally aligned carbon fibre reinforced epoxy composite is loaded as shown in the figure. The volume fraction of the fibre is 0.6. The Young’s modulus of the composite is __________ GPa.

(Given: Young’s Modulus of the fibre and the matrix are 200 GPa and 10 GPa, respectively)

Diagram for Engineering Sciences question 14

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The atoms in a gas laser have two energy levels such that a transition from the higher to the lower level releases a photon of wavelength 500 nm. If 7 × 10²⁰ atoms are pumped into the upper level with 4 × 10²⁰ atoms in the lower level, the amount of energy released in a single pulse is __________ Joules (give answer up to 2 decimal places)

(Given: Planck’s constant, h = 6.6 × 10⁻³⁴ J s; speed of light, c = 3 × 10⁸ m s⁻¹)

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The speed of an electron is measured to be 300 m s⁻¹ with an uncertainty of 0.01%. The fundamental accuracy with which the position of the electron can be determined simultaneously with the speed in the same experiment is __________ mm (give answer up to 2 decimal places)

(Given: Planck’s constant, h = 6.6 × 10⁻³⁴ J s; mass of electron = 9.1 × 10⁻³¹ kg)

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When 3 identical non-interacting spin ½ particles are put in an infinite potential well, the ground state energy of the system is 18 meV. If instead, seven particles are put inside the potential well, the new ground state energy is ________ meV.

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During deformation of a semi-crystalline polymer, with spherulitic morphology, stressed in tension, what happens to the amorphous and the crystalline regions at the later stages?

Your answerChoose one option.

Amorphous regions remain intact and only crystallites experience bending and stretching of chains

Only amorphous regions elongate in the stress direction and crystallites remain intact

Amorphous regions elongate in the stress direction and crystallites experience bending and stretching of chain

None of the above

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Which of the following statement(s) is / are true regarding the structure-property correlation in polymers? (i) Polymers that are less coiled are more crystalline than those that are more coiled (ii) Branched polymers are more crystalline than the linear ones (iii) Polymers with inter-chain interactions have higher glass transition temperature than those without inter-chain interactions (iv) Polymers with inter-chain interactions are more crystalline than those without inter-chain interactions

Your answerChoose one option.

(i) and (ii)

(i) and (iii)

(ii) and (iv)

(ii) and (iii)

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GATE XE Properties and Applications of Materials PYQs

Question 6

Question 8

Question 12

Question 13

Question 14

Question 16

Question 17

Question 18

Question 36

Question 37