Question

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l₁ and l₂
where, l₁ = nl₂
and n is an integer. The ratio k₁/k₂ of the corresponding force constants, k₁ and k₂ will be:
(A) n (B) 1/n²
(C) n² (D) 1/n

Answer 1

Answer:

D

k is inversely proportional to length

Answer 2

The ratio of k1/k2 is 1/n.

as given in question let l be initial length

l1+l2=l

and l1=nl2

therefore we get l1/l2=n

now k is directly proportional to 1/l

so k=c/l

k1=c/l1 and k2=c/l2

now k1/k=c/l1*l/c

=l/l1

=1+l2/l1

therfore k1/k=1+1/n(as we know the ratio)

now k2/k=c/l2*l/c

=l1/l2+1

=n+1

therefore k1/k2=n+1/n*(n+1)

=1/n