Determine whether the following statements are true and give an explanation or counterexample.

a. The mass of a thin wire is the length of the wire times its average density over its length.

b. The work required to stretch a linear spring (that obeys Hooke’s law) 100 cm from equilibrium is the same as the work required to compress it 100 cm from equilibrium.

c. The work required to lift a 10-kg object vertically 10 m is the same as the work required to lift a 20-kg object vertically 5 m.

d. The total force on a 10-ft² region on the (horizontal) floor of a pool is the same as the total force on a 10-ft² region on a (vertical) wall of the pool.