Mechanical Properties of Solids

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