A spherical ball contracts in volume by 0.01% when subjected to a normal uniform pressure of 100 atmospheres. Calculate the bulk modulus of a material.

Q: Compute the decrease in volume of 2.5 x 10-4 m³, of mercury when subjected to a pressure of 20 x 105…

A: Given data: mercury's volume V=2.5×10-4 m3 Pressure P=20×105 N/m2 bulk modulus β=2.8×1010N/m2

Q: A (2 m)-long steel wire in a musical instrument has a radius of (0.3 mm). When the wire is under a…

A: Length of steel wire (L) = 2 m Radius (R) = 0.3 mm Area = π×R2= π×(0.3×10-3)2 = 2.827×10-7 m2Tension…

Q: A brass rod 5ft long with a square cross section 0.5 inch on a side is used to support a 520-lb load…

A: B=F/AL'/L=FLL'AL'=FLBA F is the load L is the original length B is the bulk modulus A is the cross…

Q: A spherical ball contracts in volume by 0-01%, when subjected to a normal uniform pressure of 100…

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Q: A cube made of an unknown material has a dimension of 6 cm on all edges. If the upper face is…

A: The shear modulus of the material can be determined as, G=FLAΔx

Q: Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of…

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Q: A makeshift compact torsional spring is made of steel (Gst = 11,000,000 psi) and is composed of a…

A: Given that a  makeshift compact torsional spring is made of steel (Gst =11,000,000 psi) and is…

Q: A 19 -L volume of oil is subjected to pressure which produces a volume strain of 1.3 x L0-4. The…

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Q: A steel wire of diameter 1 mm can support a tension of 0.2 kN. Determine the diameter of a steel…

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Q: Express all answers in significant figures and scientific notation. A solid spherical material…

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Q: For safety in climbing, a mountaineer uses a nylon rope that is 50. m long and 1.0 cm in diameter.…

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Q: When the pressure on a sphere is increased by 80 atmospheres then its volume decreases by 0.01% .…

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Q: An anchor made of cast iron of bulk modulus 60.0 × 109 PA and volume of 0.230 m3, is lowered over…

A: Given  Bulk Modulus B=60×109 Pa Change in pressure ∆P=1.75 × 106 Pa. Volume V=0.230 m3

Q: If 1.0 m of concrete weighs 5.0 x 104 N, what is the height of the tallest cylindrical concrete…

A: The compression strength is given by, P=FA Here, F is the force applied and A is the area of…

Q: Find the smallest diameter bolt that can be used in the clevis in Fig. 3.2 if P = 415 kN. The…

A: Given, P=415kN Shearing strength=300Mpa

Q: What is the value of Young's modulus of rigidity of a fluid?

A: The definition of a fluid state that no matter how small a force is, no fluid can maintain…

Q: A 200 kg load is hung on a wire of length 4.00 m, cross-sectional area of 0.200×10^-4 m^2 and…

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Q: A spherical ball contracts in volume by 0.0098% when it is subjected to a pressure of 100 atmosphere…

A: The expression for the Bulk modulus is,

Q: A certain metal cube of bulk modulus 8.5 x 1010 Pa is submerged to a fluid at a certain depth. What…

A: Given Bulk modulus of the metal is given as β=8.5×1010 Pa Bulk strain is given as ∆VV=0.31%   We…

Q: Bulk modulus is the decreasing in hydrostatic pressure to the corresponding fractional decrease in…

A: Bulk modulus is the decreasing in hydrostatic pressure to the corresponding fractional decrease in…

Q: A  solid spherical material made of  rubber with was exposed  to  a  change in  pressure  of 85 Pa.…

A: Given: The change in pressure (∆P) is 85 Pa. The volume reduced to 8% of the original volume.…

Q: The longitudinal stress developed in the thin spherical shells are (a) Perpendicular to the radial…

A: Wall thickness of a thin cylindrical and spherical shell will be equal or less than the 1/20 of the…

Q: Compute the bulk modulus of water from the following data: Initial volume = 100.0 litre, Pressure…

A: Given, P = 100 atmosphere = 100 x 1.013 x 105 Pa Final volume, V2 = 100.5 l = 100.5 ×10 –3 m3…

Q: A body of mass 500 kg is suspended at the free end of an iron wire of length 3 m and cross-sectional…

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Q: A cubic industrial material whose one side is of length 2.0 cm has a bulk modulus of 4.7 x 10^5…

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Q: A cylinder of certain mass is held in vertical position. If the height of the cylinder is 10 cm and…

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Q: Compute the decrease in volume of 2.5 x 104 m³, of mercury when subjected to a pressure of 20 x 105…

A: Formula for bulk modulus can be written as,                        K = -PV∆V ---->     Change in…

Q: One end of a metal rod of radius R =8.7 mm and length L-81 cm is held in a vise, see figure. A force…

A: The expression for the Young’s modulus is,

Q: If 20 kN load is applied on a cylinder of diameter 20 mm, the stress developed in the cylinder is

A: Force = 20 KN = 20000 N Radius = 10 mm = 0.010 m AREA = πr2 = 3.14 x 0.0102 = 3.14 x 10-4 m2 Stress…

Q: For safety in climbing, a mountaineer uses a nylon rope that is 50. m long and 1.0 cm in diameter.…

A: Young’s modulus is given by,

Q: A material is 250 cm long, 8 cm wide and 10 cm deep. The material is subjected to an axial force of…

A: Given: Length of material, L = 250 cm = 2.5 m  width of material, b = 8 cm = 0.08 m  depth of…

Q: A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 x 10 9 N/m 2.…

A: The Bulk Modulus of a system is given as

Q: A 5-m high aluminum cylinder must support a load of 450 kN. If the maximum allowable stress is 0.14…

A: Given data: The height of cylinder is l=5 m. Load supported P=450 kN. Maximum allowable stress is…

Q: The pressure in an explosion chamber is 345M Pa. What would be the per cent change in volume of…

A: Let P be the pressure, B be the bulk modulus of the chamber, V be the volume.Write the expression…

Q: A 3.5 cm cube of unknown metal has a shear modulus of 5.0x 10°N/m ? absorbed a force of 0.40 N.…

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Q: Determine the volume contraction of a solid copper cube, 10cm on an edge, when subjected to a…

A: The bulk modulus is given by

Q: Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of…

A: Given, Pressure acting on the glass plate, p = 10 atm = 10 × 1.013 × 105 Pa

Q: A hydraulic press contains 0.25 m3 of oil. Find the decrease in the volume of the oil when it is…

A: Let the Bulk modulus of oil is given by B. Let the change in pressure is given by ∆p. Let the change…

Q: A 89 cm long wire was found to stretch 1.6 mm by a force of 117 N. The wire was round in the shape…

A: Given data:  Length of wire (L) = 89 cm = 0.89 m Change in length (Δl) = 1.6 mm = 1.6×10-3 m Force…

Q: How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume…

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Q: What is rigidity modulus of a liquid?

A: Step 1Modulus of rigidity is defined usually as the ratio of shear stress to shear strain. More…

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).