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Mechanical Properties of Solids MCQs for NEET — Physics Questions with Answers

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k is the force constant of a spring what will be the work done in increasing its extension form $l_1 to l_2$ be ?

A. $ k (l_1 -l_2 ) $ B. $ {k \over 2 } (l_2 + l_1 ) $ C. $ k (l_2^2 -l_1^2 ) $ D. $ {k \over 2} (l_2^2 -l_1^2 ) $

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Explanation

At extension $l_1$ the stored energy = $ {1 \over 2 } kl_1^2 $ $ \therefore$ At extension $ l_2 $ the stored energy = ${1 \over 2} kl_1^2 $ Work done in increasing its extension from $l_1 to l_2 $ =$ {1 \over 2} k ( l_2 ^2 - l_1 ^2 ) $

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When a 4 kg mass is hung vertically on a light spring that obeys Hook's law, the spring stretches by 2 cm what will be the work required to be done by an external agent in stretching this spring by 5 cm ?

A. 4.900 Joule B. 2.450 Joule C. 0.495 Joule D. 0.245 Joule

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Explanation

K = F/X

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The isothermal elasticity of a gas is equal to....................

A. Density B. Volume C. Pressure D. Specific heat

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Explanation

Isothermal elasticity ki = p

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If the volume of a block of aluminium is decreased, bythe pressure (stress) on its surface is increased by.................$ (Bulk modulus of A l = 7.5 \times 10 ^ {10 } Nm^{-2} )$

A. $ 7.5 \times 10 ^{10} N/m^2 $ B. $ 7.5 \times 10 ^{8} N/m^2 $ C. $ 7.5 \times 10 ^{6} N/m^2 $ D. $ 7.5 \times 10 ^{4} N/m^2 $

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Explanation

$ B = { -PV \over \triangle Y } \Rightarrow P = - { \triangle V \times B \over V } $ $ given { -\triangle V \over V } = 1\% = {1 \over 100} $ $ P = { 1.5 \times 10^{10} \over 100 } = 1.5 \times 10^8 N/m^2 $

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If a rubber ball is taken at the depth of 200min a pool, Its volume decreases by 0.1% . If the density of the water is $ 1 \times 10 ^ 3 kg /m^3 and g = 10 m/s^2 $ . Then waht will be the volume elasticity in $ N /m^2 $ ?

A. $ 10 ^ 8 $ B. $ 2 \times 10 ^8 $ C. $ 10 ^ 9 $ D. $ 2 \times 10 ^ 9 $

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Explanation

$ k = { \triangle P \over { \triangle v \over v } } = { hsg \over { \triangle v \over v} } $

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The pressure applied from all directions on a cube is p. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is B and the coefficient of volume expansion is $ \alpha $

$ { P \over \alpha \beta } $

$ { P \alpha \over \beta } $

$ { \beta p \over \alpha } $

$ { \alpha \beta \over p } $

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Explanation

If the coefficient of volume expansion and raise in temprature is $ \triangle \theta $ then $ \triangle v = v \alpha \triangle \theta $ $ \Rightarrow { \triangle v \over v } = \alpha \triangle \theta $ volume elasticity $ \beta = { P \over { \triangle v \over v }} = { P \over \alpha \triangle \theta } $

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A uniform cube is subjected to volume compression. If each side is decreased by 1% Then what is bulk strain ?

A. 0.01 B. 0.06 C. 0.02 D. 0.03

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Explanation

If side of the cube is L then V =$ L^ 2$ $$ \Rightarrow { dv \over v } = { 3dL \over L } $$ $ \% change in voulume = 3 \times (\% change in length) = 3 \times 1\% = 3\% $ $ \therefoe Bulk modulus = { \triangle v \over v } = 0.03 $

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The ratio of two specific heats of gas $ { C_p \over C_v } $ for Argon is 1.6 and for hydrogen is 1.4. Adiabatic elasticity of Argon at pressure p is E. Adiabatic elasticity of hydrogen will also be equal to E at the pressure.

A. p B. 7/8 p C. 8/7 P D. 1.4 P

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Explanation

$ Adiabatic elasticity \varepsilon = vp $ $ For Argon EA_r = 1.6 p$ $For hydrogon EH_2 = 1.4 pl$ As elasticityof hydrogen & Argon are equal $ \therefore 1.6 P = 1.4 Pl $ $ \therefore P' = 8/7 P $

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What is the isothermal bulk modulus of a gas at atmospheric pressure ?

A. 1 mm of Hg B. 13.6 mm of Hg C. $ 1.013 \times N / m^2 $ D. $ 2.026 \times 10 ^ 5 N/m^2 $

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Explanation

Isothermal elasticity P = Ki = 1 atm = 1.013 = $ 1.013 \times 10^5 N/m^2 $

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The bulk modulus of an ideal gas at constant temperature.........

A. is equal to its volume V B. is equal to P/2 C. is equal to its pressure P D. cannot be determined

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Explanation

Isothermal bulk modulus = pressure of gas

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