spring has length T and spring constant ‘k It is ut into two pieces of lengths lv and Z2, such that = nlr The force constant of the spring of length is

The spring constant (k) of a spring is inversely proportional to its natural length (L), such that kL = constant. For an original spring of length L and constant k, if it is cut into two pieces of lengths l1 and l2, the new spring constants k1 and k2 are determined by the relation kL = k1l1 = k2l2 [t1][t3]. Given the total length L = l1 + l2 and the condition l1 = n*l2, we can substitute to find l2 = L/(n+1) and l1 = nL/(n+1). To find the force constant of the piece with length l2 (implied by the context of finding the constant for a specific piece in such problems), we use k2 = k(L/l2). Substituting l2, we get k2 = k(L / (L/(n+1))) = k(n+1). If the question asks for the piece of length l1, k1 = k(L/l1) = k(n+1)/n. However, standard physics problems of this type typically seek the constant for the smaller segment or the general relation k(n+1) [t2]. Option 1 matches the derivation for the segment where length is reduced by a factor of (n+1).