Length of a spring of force constant k in its unstretched condition is l. The spring is cut into two parts which have their unstretched lengths in the ratio l1:l2=q:1. Force constants of the two parts k1 and k2 are then:

A
$k (q + 1), kq$
B
$k \frac{(q + 1)}{q}, kq$
C
$k \frac{(q + 1)}{q}, k (q + 1)$
D
$k \frac{(q - 1)}{q}, k \frac{(q + 1)}{q}$

Solution:

$l_{1} + l_{2} = l As l_{1} = {ql}_{2}$
$∴ l_{2} = \frac{l}{q + 1} and l_{1} = \frac{ql}{q + 1} k_{1} = \frac{mg}{l_{1}} = \frac{mg (q + 1)}{ql} = \frac{k (q + 1)}{q} k_{2} = \frac{mg}{l_{2}} = \frac{mg}{l_{2}} (q + 1) = k (q + 1)$

Length of a spring of force constant k in its unstretched condition is l. The spring is cut into two parts which have their unstretched lengths in the ratio $l_{1} : l_{2} = q : 1$ . Force constants of the two parts k₁ and k₂ are then:

Solution:

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