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Mechanical Properties of Solids

What is the value of one torr in Pascal?

1 torr = 133 Pascal

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What is bar?

Bar is the unit of pressure and is equal to 10⁵ Pascal.

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A cube of side 10cm made from lead is fixed at one face. When a tangential force of 334kN is applied on the opposite face, it gets displaced by 0.6mm. Find the shear modulus of lead.

$Given comma space Tangential space Force comma space straight F space equals space 334 space kN space equals space 334000 space straight N space Side space of space the space cube comma space straight l space equals space 10 space cm space equals space 0.1 space straight m space Area space of space the space face space over space which space the space force space is space applied comma space straight a space equals space straight L squared space equals space 0.1 space cross times space 0.1 space equals space 10 to the power of negative 2 end exponent space straight m squared Displacement comma space increment straight l space equals space 0.6 space mm space equals space 6 space cross times space 10 to the power of negative 4 end exponent space straight m space Therefore comma space Shear space modulus comma space straight eta space equals space fraction numerator FL over denominator straight a increment straight L end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 334000 cross times 0.1 over denominator 10 to the power of negative 2 end exponent cross times 6 space cross times space 10 to the power of negative 4 end exponent end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 55.67 space cross times 10 to the power of 10 space straight N divided by sq. straight m$

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Three vessels have same base area. These vessels are filled to same height by same liquid. In which vessel will the force on the base be maximum?

As all the vessels are filled with same liquid to the same height, therefore the pressure due to height column at the base will be the same. Also, since the base area of all the vessels is same, therefore the force acting on all the base of all vessels will be the same.

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The volume of a spherical body is decreased by10^–3% when it is subjected to pressure of 40 atmospheres. Find the bulk modulus of body.

(1 Atmosphere pressure =1.01x10⁵ N/m²).

Volume of a spherical body decreased = 10^-3 %Pressure, P = 40 atm

We know,
Bulk modulus, $K = - V \frac{dP}{dV}$

Percentage change in volume is given by 10^-3%

$∴ \frac{ΔV}{V} = \frac{10^{- 3}}{100} = 10^{- 5} T h e r e f o r e, K = \frac{40 \times 1.01 \times 10^{5}}{10^{- 5}} = 4.04 \times 10^{11} N / m^{2}$

is the bulk modulus of the body.

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Mechanical Properties of Solids

The volume of a spherical body is decreased by10^–3% when it is subjected to pressure of 40 atmospheres. Find the bulk modulus of body.

(1 Atmosphere pressure =1.01x10⁵ N/m²).

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Mechanical Properties of Solids

The volume of a spherical body is decreased by10–3 % when it is subjected to pressure of 40 atmospheres. Find the bulk modulus of body. (1 Atmosphere pressure =1.01x105 N/m2).

The volume of a spherical body is decreased by10^–3% when it is subjected to pressure of 40 atmospheres. Find the bulk modulus of body.

(1 Atmosphere pressure =1.01x10⁵ N/m²).