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# If a force of 50N stretches a wire from 20m to 20.01m, what is the amount of for...

### Question

If a force of 50N stretches a wire from 20m to 20.01m, what is the amount of force required to stretch the same material from 20m to 20.05m?

A) 250N

B) 200N

C) 100N

D) 50N

### Explanation:

Original length = 20m
first new length = 20.01m

first increase in length = 20.01m - 20m = 0.01m

Second new length = 20.05m
second increase in length = 20.05 - 20m = 0.05m

From hooke's law = $$\frac{F_1}{e_1} = \frac{F_2}{e_2} \implies \frac{50}{0.01} = \frac{F_2}{0.05} \\ \implies F_2 = \frac{50 \times 0.05}{0.01} = 250N$$

## Dicussion (1)

• Original length = 20m
first new length = 20.01m

first increase in length = 20.01m - 20m = 0.01m

Second new length = 20.05m
second increase in length = 20.05 - 20m = 0.05m

From hooke's law = $$\frac{F_1}{e_1} = \frac{F_2}{e_2} \implies \frac{50}{0.01} = \frac{F_2}{0.05} \\ \implies F_2 = \frac{50 \times 0.05}{0.01} = 250N$$