Assertion A spring of force constant k is cut into two pieces having lengths in the ratio 1 :2. The force constant of series combination of the two parts is (3 k/2). Reason The spring connected in series are represented by k=k1+k2

Question

Assertion A spring of force constant k is cut into two pieces having lengths in the ratio 1 :2. The force constant of series combination of the two parts is (3 k/2). Reason The spring connected in series are represented by k=k1+k2 (A) Both assertion and reason are true and reason is the correct explanation of assertion (B) Both assertion and reason are true but reason is not the correct explanation of assertion (C) Assertion is true but reason is false. (D) Both assertion and reason are false.

Tardigrade Admin · Accepted Answer

k=(f/l) ⇒ k propto (1/l) ⇒ (k1/k2)=(l2/l1)=(2/1) k1=2 k, k2=k In series, (1/k')=(1/k1)+(1/k2) =(1/2 k)+(1/k)=(3/2 k) ∴ k'=2 / 3 k

Q. Assertion A spring of force constant $k$ is cut into two pieces having lengths in the ratio $1 : 2$ . The force constant of series combination of the two parts is $\frac{3 k}{2}$ .
Reason The spring connected in series are represented by $k = k_{1} + k_{2}$

Both assertion and reason are true and reason is the correct explanation of assertion

Both assertion and reason are true but reason is not the correct explanation of assertion

Assertion is true but reason is false.

Both assertion and reason are false.

$k = \frac{f}{l}$
$\Rightarrow k \propto \frac{1}{l}$
$\Rightarrow \frac{k _{1}}{k _{2}} = \frac{l _{2}}{l _{1}} = \frac{2}{1}$
$k_{1} = 2 k, k_{2} = k$
In series, $\frac{1}{k ^{'}} = \frac{1}{k _{1}} + \frac{1}{k _{2}}$
$= \frac{1}{2 k} + \frac{1}{k} = \frac{3}{2 k}$
$∴ k^{'} = 2/3 k$

Q. Assertion A spring of force constant k is cut into two pieces having lengths in the ratio 1:2. The force constant of series combination of the two parts is 23k​. Reason The spring connected in series are represented by k=k1​+k2​