Mechanical Properties of Solids

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be . [Area of cross section of wire =0.005 cm2, Y=2 1011 Nm-2 and g=10 ms-2]

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02\% is m. (Take density of sea water =103 kgm-3, Bulk modulus of rubber =9 108 Nm-2, and g=10 ms-2)

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0 10-5 m and Young's modulus of the metal is 2.0 1011 N/m2. The longitudinal strain developed in the wire is 1 . The value of is . [Use g=10 m/s2] [figure]

Young's modulus of material of a wire of length 'L' and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young's modulus will be :

1. 4 Y
2. 2 Y
3. Y4
4. Y

Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm2 and Young's modulus 2 1011 N m-2. Neglecting friction, the longitudinal strain on wire B is 10-4. (Take g=10 m/s2) [figure]

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

1. 2 times
2. 4 times
3. 3 times
4. 32 times

Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4:1 and force F1 is applied to P, an extension of l is produced. The force which is required to produce same extension in Q is F2. The value of F1F2 is .

If average depth of an ocean is 4000 m and the bulk modulus of water is 2 109 N m-2, then fractional compression VV of water at the bottom of ocean is 10-2. The value of is (Given, g = 10 m s-2, = 1000 kg m-3)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

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