EASY
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Shear Modulus (Modulus of rigidity) is defined as the ratio of shear stress to the shear strain.
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Important Questions on Mechanical Properties of Solids
MEDIUM
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:
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:
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?
MEDIUM
What is the pressure required to reduce the given volume of water by ? (Bulk modulus )
HARD
In plotting stress versus strain curves for two materials and , a student by mistake puts strain on the -axis and stress on the - axis as shown in the figure. Then the correct statement(s) is(are)
MEDIUM
A rubber cord has a cross-sectional area and total unstretched length . It is stretched to and then released to project a particle of mass . The velocity of projection is [Given, Young's modulus of rubber, ]
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
MEDIUM
One end of thick horizontal copper wire of length and radius is welded to an end of another thin horizontal copper wire of length and radius . When they are stretched by applying same force at two ends, the ratio of the elongation in the thick wire to that in thin wire is
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:
MEDIUM
The bulk modulus of a spherical object is . If it is subjected to uniform pressure , the fractional decrease in radius is
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)
MEDIUM
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
String of unstretched length is stretched by applying a force at the mid-point such that the segments and make an angle with as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio . The force is given by
MEDIUM
The elastic limit of brass is . The minimum diameter of a brass rod if it is to support a load without exceeding its elastic limit will be
HARD
A uniform cylindrical rod of length , area of cross-section and Young's modulus is acted upon by the forces as shown in the figure. The elongation of the rod is
MEDIUM
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)
MEDIUM
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,
MEDIUM
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:
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:
MEDIUM
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:
