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A student performs an experiment to determine the Young's modulus of a wire, exactly 2m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of 0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of 0.01 mm. Take (exact). The Young's modulus obtained from the reading is
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Important Questions on Properties of Solids and Liquids
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The decrease in length of a metal bar of length and cross-sectional area when compressed with a load along its length is ( Young's modulus of the material of metal bar)
EASY
The value of in the graph gives
MEDIUM
A steel rail of length and area of cross section is prevented from expanding along its length while the temperature rises by . If coefficient of linear expansion and Young's modulus of steel are and respectively, the force developed in the rail is approximately:
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A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere , is:
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A load of mass is suspended from a steel wire of length and radius in Searle's apparatus experiment. The increase in length produced in the wire is Now the load is fully immersed in a liquid of relative density The relative density of the material of load is The new value of increase in length of the steel wire is:
EASY
In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :
EASY
A rubber cord of density Young's modulus and length is suspended vertically. If the cord extends by a length under its own weight, then is
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Young's moduli of two wires and are in the ratio . Wire is long and has radius Wire is long and has radius If the two wires stretch by the same length for a given load, the value of is close to:
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The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:
HARD
An external pressure is applied on a cube at so that it is equally compressed from all sides. is the bulk modulus of the material of the cube and is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:
HARD
A uniformly tapering conical wire is made from a material of Young's modulus and has a normal, unextended length . The radii, at the upper and lower ends of this conical wire, have values and , respectively. The upper end of the wire is fixed to a rigid support and a mass is suspended from its lower end. The equilibrium extended length, of this wire, would equal:
EASY
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area and the second wire has cross-sectional area If the length of the first wire is increased by on applying a force how much force is needed to stretch the second wire by the same amount?
HARD
A bottle has an opening of radius and length . A cork of length and radius where , is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is and the coefficient of friction between the bottle and cork is , then the force needed to push the cork into the bottle is
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The bulk modulus of a spherical object is . If it is subjected to uniform pressure , the fractional decrease in radius is
HARD
A thin long rod has a radius of . A force of is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is , which of the following statements is false?
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A wire is stretched such that its volume remains constant. The Poisson’s ratio of the material of the wire is:
EASY
Copper of fixed volume is drawn into wire of length . When this wire is subjected to a constant force the extension produced in the wire is Which of the following graph is a straight line?
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A metal rod of length and cross-sectional area is heated through . What is the force required to prevent the expansion of the rod lengthwise?
= Young's modulus of the material of rod, coefficient of linear expansion
HARD
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to . If the Young's modulus of the material of the wire is , then is equal to:
(gravitational acceleration)
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The length of elastic string obeying Hooke's law is metres when the tension is and metres when the tension is . The length in metres when the tension is is,
