A spring 60cm long streached by 2cm by the application of load 200gm what will be the length when a load of 500gm is applied?
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Explanation:
ɢɪᴠᴇɴ☆
A spring 60 cm long stretched by 2 cm when 200 gram load is applied.
☆ᴛᴏ ғɪɴᴅ☆
Length of spring when 500 gram load is applied.
☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆
Here,
\to l_0 = 60\:cm→l
0
=60cm
\to F_1 = 0.2g = 1.96N, x_1 = 2\: cm→F
1
=0.2g=1.96N,x
1
=2cm
\to F_2 = 0.5g = 4.9N→F
2
=0.5g=4.9N
Force and displacement in a spring are related as
\to F = kx→F=kx
\to 1.98N = k\times 2\: cm→1.98N=k×2cm
\to \boxed{ k = 0.98\:N/cm}→
k=0.98N/cm
Applying this equation in the second case,
\to 4.9N = (0.98\:N/cm)\times x_2→4.9N=(0.98N/cm)×x
2
\to x_2 =\frac{4.9N}{0.98\:N/cm}→x
2
=
0.98N/cm
4.9N
\to \boxed{x_2 = 5\:cm}→
x
2
=5cm
Therefore, lotal length of the spring,
\to l = l_0 + x_2→l=l
0
+x
2
\to l = 60 + 5→l=60+5
\to \boxed{l = 65\:cm}→
l=65cm
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