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:
A steel wire of diameter and Young's modulus carries a load of mass . The length of the wire with the load is . A vernier scale with divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count , is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by , the vernier scale division which coincides with a main scale division is __________. Take .
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:
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:
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
Two separate wires and are stretched by and respectively, when they are subjected to a force of Assume that both the wires are made up of same material and the radius of wire is times that of the radius of wire The length of the wires and are in the ratio of Then can be expressed as , where is _____.
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:
Speed of a transverse wave on a straight wire (mass length and area of cross-section is . If the Young's modulus of wire is , the extension of wire over its natural length is:
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)
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:
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:
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:
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?
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)
A steel wire of cross-sectional area has elastic limit of . The maximum upward acceleration that can be given to a elevator supported by this steel wire if the stress is to exceed one-fourth of the elastic limit is [Take, ]
One end of a horizontal thick copper wire of length and radius is welded to an end of another horizontal thin copper wire of length and radius. When the arrangement stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
