The diagram shows a force-extension graph for a rubber band. Consider the following statements:
I. It will be easier to compress this rubber than expand it.
II. Rubber does not return to its original length after it is stretched.
III. The rubber band will get heated if it is stretched and released.
Which of these can be deduced from the graph?
(1) III only
(2) II and III
(3) I and III
(4) I only
Which of the following relation is true?
(1)
(2)
(3)
(4)
A steel ring of radius r and cross-sectional area A is fitted onto a wooden disc of radius R(R>r). If the Young's modulus of steel is Y, then the force with which the steel ring is expanded is :
(1) AY (R/r)
(2) AY (R - r)/r
(3) (Y/A)[(R-r)/r]
(4) Yr/AR
A metal wire of length and area of cross-section A is attached to a rigid support. Another metal wire of length and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If are the young's moduli of the wires respectively, the effective force constant of the system of two wires is :
(1)
(2)
(3)
(4)
A light rod of length 2m suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight W is hung from a light rod as shown in the figure. The rod hung by means of a steel wire of cross-sectional area and brass wire of cross-sectional area . To have equal stress in both wires, =?
(1) 1/3
(2) 1/4
(3) 4/3
(4) 1/2
The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is:
(1) 1%
(2) 2%
(3) 2.5%
(4) 4%
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 the area a floats on the surface of the liquid, covering an entire cross-section of the cylindrical containers. 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:
(1)
(2)
(3)
(4)
From a steel wire of density is suspended a brass block of density . The extension of steel wire comes to e. If the brass block is now fully immersed in a liquid of density , the extension becomes e'. The ratio will be :
(1)
(2)
(3)
(4)
One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and weight is suspended from the looser end. If A is the area of cross-section of the wire, the stress in the wire at a height from the upper end is :
(1)
(2)
(3)
(4)
A massless rod of length L is hanging from a horizontal ceiling with help of two wires, of equal lengths and diameters, attached to the ends of the rod. The Young's modulus of the first wire is Y and the second wire is 1.2Y. A mass M is attached to the rod at a distance X from the first wire. If the stretching of the two wires is equal, then X/L is
(1)
(2)
(3)
(4)
A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up and recast into a solid rod of the same length. The ratio of the torsional rigidities of the circular tube and the solid rod is :
(1)
(2)
(3)
(4)
A steel wire is suspended vertically from a rigid support. When loaded with a weight in the air, it extends by and when the weight is immersed completely in water, the extension is reduced to . Then the relative density of the material of the weight is :
(1)
(2)
(3)
(4)
For a given material, the Young's modulus is 2.4 times that of rigidity modulus. Its Poisson's ratio is :
(1) 2.4
(2) 1.2
(3) 0.4
(4) 0.2
The upper end of a wire of diameter 12 mm and length 1 m is clamped and its other end is twisted through an angle of . The angle of shear is :
(1)
(2)
(3)
(4)
The system is rotated with the angular speed (see figure). What is the ratio of energy stored in each wire?
(1) 31:9
(2) 50:9
(3) 47:9
(4) 8:9