Question

A steel wire of diameter 2 mm has a breaking
strength of 4 x 105 N. What is the breaking force
of similar steel wire of diameter 1.5 mm?
(1) 2.3 × 105N (2) 2.6 x 105N
(3) 3 * 105 N
(4) 1.5 * 105 N​

Answer 1

Explanation:

We know that breaking strength is the force acting per unit area.

Hence,

$\: breaking \: strength = \frac{force}{area}$

$4 \times 10 {}^{5} = \frac{f}{\pi \times 10 {}^{ - 6} }$

$f = 4\pi \times 10 {}^{ - 1}$

Now breaking strength of wire having diameter 1.5mm

$breaking \: strengh \: = \frac{4\pi \times 10 {}^{ - 1}}{\pi \times 10 {}^- 6 \times (.75 \: ) }$

Answer will be 5.3×10^5