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 Answer: Option C
Explanation
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 )