Q. No.A cube has side length \(5 ~\text {cm}\) and modulus of rigidity \(10^5 ~\text{N/m}^2 .\) The displacement produced by a force of \(10 ~\text N\) in the upper face of cube is: (in mm)
1. \(5\)
2. \(3\)
3. \(2\)
4. \(6\)
1. \(5\)
2. \(3\)
3. \(2\)
4. \(6\)
Subtopic: Shear and bulk modulus |
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A cylindrical rod of length \(1 ~\text m\) and radius \(4 ~\text{cm}\) is mounted vertically. It is subjected to a sheer force of \(10^5 ~\text{N}\) at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement \(\theta\) of the rod axis from its original position would be: (shear moduli, \(G = 10^{10} ~\text{N/m}^2\))
1. \(\dfrac{1}{2\pi}\)
2. \(\dfrac{1}{160\pi}\)
3. \(\dfrac{1}{4\pi}\)
4. \(\dfrac{1}{40\pi}\)
1. \(\dfrac{1}{2\pi}\)
2. \(\dfrac{1}{160\pi}\)
3. \(\dfrac{1}{4\pi}\)
4. \(\dfrac{1}{40\pi}\)
Subtopic: Shear and bulk modulus |
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Two slabs with square cross section of different materials \((1, 2)\) with equal sides \((l)\) and thickness \(d_1\) and \(d_2\) such that \(d_2 = 2d_1 \) and \(l > d_2.\) Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \(\theta_2 = 2\theta_1.\) If the shear moduli of material \(1\) is \(4 \times 10^9 \text{ N/m}^2 , \) then shear moduli of material \(2\) is \(x \times 10^9~ \text{N/m}^2 ,\) where value of \(x\) is:
1. \(1\)
2. \(2\)
3. \(5\)
4. \(6\)
1. \(1\)
2. \(2\)
3. \(5\)
4. \(6\)
Subtopic: Shear and bulk modulus |
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A sample of a liquid is kept at \(1~ \text{atm.}\) It is compressed to \(5~\text{atm} \) which leads to change of volume of \(0.8~\text{cm}^3 .\) If the bulk modulus of the liquid is \(2\) \(\text{GPa,}\) the initial volume of the liquid was: (in litre) (Take \(1~ \text{atm} = 10^5~\text{Pa}\))
1. \(6\)
2. \(8\)
3. \(10 \)
4. \(4\)
1. \(6\)
2. \(8\)
3. \(10 \)
4. \(4\)
Subtopic: Shear and bulk modulus |
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The increase in pressure required to decrease the volume of a water sample by \(0.2\%\) is \(P×10^5~\text {NM}^{-2}.\) The bulk modulus of water is \(2.15 × 109~ \text { Nm}^ {-2}\). The value of \(P\) is:
1. \(79\)
2. \(43\)
3. \(28\)
4. \(134\)
1. \(79\)
2. \(43\)
3. \(28\)
4. \(134\)
Subtopic: Shear and bulk modulus |
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The volume contraction of a solid copper cube of edge length \(10~\text{cm},\) when subjected to a hydraulic pressure of \(7 \times 10^6~\text{Pa} \) would be:
(Given the bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{Nm}^{-2}\))
1. \(150~\text{mm}^3\)
2. \(50~\text{mm}^3\)
3. \(125~\text{mm}^3\)
4. \(108~\text{mm}^3\)
(Given the bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{Nm}^{-2}\))
1. \(150~\text{mm}^3\)
2. \(50~\text{mm}^3\)
3. \(125~\text{mm}^3\)
4. \(108~\text{mm}^3\)
Subtopic: Shear and bulk modulus |
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The fractional compression \((ΔV/V) \) of water at the depth of \(2.5~\text{km}\) below the sea level is: (in \(\%\))
(Given, the Bulk modulus of water \(= 2 × 10^9~\text{N/m}^2\), density of water \(=10^{3}~\text{kg/m}^3\), acceleration due to gravity \(g = 10 ~\text{m/s}^2\))
1. \(1.5\)
2. \(1.0\)
3. \(1.75\)
4. \(1.25\)
(Given, the Bulk modulus of water \(= 2 × 10^9~\text{N/m}^2\), density of water \(=10^{3}~\text{kg/m}^3\), acceleration due to gravity \(g = 10 ~\text{m/s}^2\))
1. \(1.5\)
2. \(1.0\)
3. \(1.75\)
4. \(1.25\)
Subtopic: Shear and bulk modulus |
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A sphere of small size is at the bottom of a lake of depth \(200 ~\text m.\) Due to pressure its fractional change in volume is \(\alpha\times 10^{-7}.\) What is the value of \(\alpha,\) if the bulk modulus of the sphere is \(5 × 10^{12}~\text{Pa}?\) (use \(g = 10 ~\text{m/s}^2\) )
1. \(5\)
2. \(4\)
3. \(6\)
4. \(10\)
1. \(5\)
2. \(4\)
3. \(6\)
4. \(10\)
Subtopic: Shear and bulk modulus |
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The bulk modulus of a liquid is \(3\times10^{10}\) Nm–2. The pressure required to reduce the volume of liquid by \(2\text{%}\) is:
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
Subtopic: Shear and bulk modulus |
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A square aluminium (shear modulus is \(25\times10^{9}~\text{Nm}^{-2}\)) slab of side \(60~\text{cm}\) and thickness of \(15~\text{cm}\) is subjected to a shearing force (on its narrow face) of \(18.0\times10^{4}~\text {N}.\) The lower edge is riveted to the floor. The displacement of the upper edge is:
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
Subtopic: Shear and bulk modulus |
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