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 :

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) (1/n2) (B) n2 (C) (1/n) (D) n

Tardigrade Admin · Accepted Answer

k1 = (C/ℓ1) k2 = (C/ℓ2) (k1/k2) = (Cℓ2/ℓ1 C) ℓ2 = (ℓ2/nℓ2) = (1/n)

Q. A spring whose unstretched length is $l$ has a force constant $k$ . The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1}$ = $n l_{2}$ and $n$ is an integer. The ratio $k_{1} / k_{2}$ of the corresponding force constants, $k_{1}$ and $k_{2}$ will be :

$\frac{1}{n ^{2}}$

$n^{2}$

$\frac{1}{n}$

$n$

$k_{1} = \frac{C}{ℓ _{1}}$
$k_{2} = \frac{C}{ℓ _{2}}$
$\frac{k _{1}}{k _{2}} = \frac{C ℓ _{2}}{ℓ _{1} C} ℓ_{2} = \frac{ℓ _{2}}{n ℓ _{2}} = \frac{1}{n}$

Q. 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 :

n21​

n2

n1​

n

k1​=ℓ1​C​ k2​=ℓ2​C​ k2​k1​​=ℓ1​CCℓ2​​ℓ2​=nℓ2​ℓ2​​=n1​

Q. A spring whose unstretched length is $l$ has a force constant $k$ . The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1}$ = $n l_{2}$ and $n$ is an integer. The ratio $k_{1} / k_{2}$ of the corresponding force constants, $k_{1}$ and $k_{2}$ will be :

$\frac{1}{n ^{2}}$

$n^{2}$

$\frac{1}{n}$

$n$

$k_{1} = \frac{C}{ℓ _{1}}$
$k_{2} = \frac{C}{ℓ _{2}}$
$\frac{k _{1}}{k _{2}} = \frac{C ℓ _{2}}{ℓ _{1} C} ℓ_{2} = \frac{ℓ _{2}}{n ℓ _{2}} = \frac{1}{n}$