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The force constant of a spring of length...

The force constant of a spring of length l is k. the spring is cut into two parts of lenghts `l_1` and `l_2`. IF `l_1=nl_2`, then find the spring constants `k_1` and `k_2` of the two parts.n is an integer.

Text Solution

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According to the problem
`l=l_1+l_2=l_1+l_1/n=l_1((n+1)/n)`
Again, `l=l_1+l_2=nl_2+l_2=l_2(n+1)`
We know that for a particular spring, the force constant is inversely proportional to the length.
`therefore k prop 1/l ` or, kl= constant
`thereforek_1l_1=kl=kl_1((n+1))/nor,k_1=k/n(n+1)`
Similarly, `k_2l_2=kl=kl_2(n+1)or,k_2=k(n+1)`
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