Am elastic material has a length of 36cm when a... - JAMB Physics 2005 Question
Am elastic material has a length of 36cm when a load of 40N is hung on it and a length of 45cm when a load of 60N is hung on it. The original length of the string is
A
12cm
B
20cm
C
18cm
D
15cm
correct option: c
For Hooke's law F = Ke
\( \implies F/e = K \\
f1/e1=f2/e2 \\
\text{Let the original length} = t_0 \\
\text{therefore} e1 = (36 - t_0)cm ; e2 = (46 - t_0)cm \\ \text{if f1} = 40N \text{f2} = 60N \\ \text{Then } \frac{40}{36 - t_0} = \frac{60}{45 - t_0} \\ \implies 40(45 - t_0) = 60(36 - t_0) \\ \text{therefore } 1800 - 40t_0 \\
2160 - 60t_0 \\ 60t_0 - 40t_0 = 2160 - 1800 \\ 20t_0 = 360 \
t_0 = 18cm \)
\( \implies F/e = K \\
f1/e1=f2/e2 \\
\text{Let the original length} = t_0 \\
\text{therefore} e1 = (36 - t_0)cm ; e2 = (46 - t_0)cm \\ \text{if f1} = 40N \text{f2} = 60N \\ \text{Then } \frac{40}{36 - t_0} = \frac{60}{45 - t_0} \\ \implies 40(45 - t_0) = 60(36 - t_0) \\ \text{therefore } 1800 - 40t_0 \\
2160 - 60t_0 \\ 60t_0 - 40t_0 = 2160 - 1800 \\ 20t_0 = 360 \
t_0 = 18cm \)
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