Question

A light wire of length l (figure – 1) is cut into two pieces in two different ways as shown in (figure – 2 & 3). Different pieces can be arranged in place of wire as shown and a load can be placed on the massless hanger. Choose the correct statements(s) : -

• A. The load required to break the wire B’ is 6 times that required to break B
• B. The stress required to break the wire B and C is same but to break B and B’ is different
• C. The stress required to break C and C’ is same
• D. The load required to break A and B’ is same, but different for B and B’

Answer 1

Answer: (C), (D)

The correct options are
C The stress required to break C and C’ is same
D The load required to break A and B’ is same, but different for B and B’

Breaking stress is the stress at which rupture occurs in a material. It depends on the material of the wire. Thus, the stress required to break C and C’ is same.

Hence option (C) is correct.
Load = stress $\times$ Cross-sectional area

For the same breaking stress, we have,

Load $\propto$ Cross-sectional area

As the area of the cross-section for A and B’ is the same therefore the load required to break A and B’ is the same.

But, as the area of the cross-section for B and B’ is not the same therefore the load required to break B and B’ is not the same.

Hence option (D) is correct.