The wires A and B shown in the figure are made of the same material, a

1.	The wires A and B shown in the figure are made of the same material, and have radii rA and rB respectively. The block between them has a mass m. When the force F is mg/3, one of the wires breaks.(a) A will break before B if rA = rB. (b) A will break before B if rA < 2rB. (c) Either A or B may break if rA = 2rB. (d) The lengths of A and B must be known to predict which wire will break.
Answer» Correct Answer is: (a, b, c) Tension in B = T_B + mg/3. Tension in A = T_A = T_B + mg = 4mg/3. ∴ T_A = 4T_B. Stress T/πr² = S. Wire breaks when S = breaking stress. For r_A = r_B, S_A = 4S_B. ∴ A breaks before B. For r_A = 2r_B, S_B = T_B/πr_B². S_A = T_A/πr_A² = 4T_B/π(2r_B)² = TB/πr_B² = S_B. As the stresses are equal, either may break.

The wires A and B shown in the figure are made of the same material, and have radii rA and rB respectively. The block between them has a mass m. When the force F is mg/3, one of the wires breaks.(a) A will break before B if rA = rB. (b) A will break before B if rA < 2rB. (c) Either A or B may break if rA = 2rB. (d) The lengths of A and B must be known to predict which wire will break.

Answer»

Correct Answer is: (a, b, c)

Tension in B = T_B + mg/3.

Tension in A = T_A = T_B + mg = 4mg/3.

∴ T_A = 4T_B.

Stress T/πr² = S. Wire breaks when S = breaking stress.

For r_A = r_B, S_A = 4S_B. ∴ A breaks before B.

For r_A = 2r_B, S_B = T_B/πr_B².

S_A = T_A/πr_A² = 4T_B/π(2r_B)² = TB/πr_B² = S_B.

As the stresses are equal, either may break.