Mechanical Properties of Solids

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8 108 N m-2 and 2 1011 N m-2, is:

1. 4 mm
2. 0.4 mm
3. 40 mm
4. 8 mm

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is :

1. W/A
2. W/2A
3. Zero
4. 2W/A

In the light of the above statements, choose the most appropriate answer from the options given below:

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true and (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changed to L1 when mass M is suspended from its free end. The expression for Young's modulus is :

1. Mg(L1 - L)AL
2. MgLAL1
3. MgLA(L1 - L)
4. MgL1AL

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l). The elastic potential energy stored in the extended wire is :

1. Mgl
2. MgL
3. 12Mgl
4. 12MgL

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by l on applying a force F, how much force is needed to stretch the second wire by the same amount?

1. 6F
2. F
3. 9F
4. 4F

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'P', the fractional decrease in radius is

1. B3P
2. 3PB
3. P3B
4. PB

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

1. 4 : 1
2. 1 : 1
3. 1 : 2
4. 2 : 1

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 10-11 Pa-1 and density of water is 103 kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?

1. 1.2 10-2
2. 1.4 10-2
3. 0.8 10-2
4. 1.0 10-2

Copper of fixed volume V is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is l. Which of the following graphs is a straight line ?

1. l versus 1l
2. l versus l2
3. l versus 1l2
4. l versus l