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 $\frac{3 k}{2}$.
Reason The spring connected in series are represented by $k=k_{1}+k_{2}$

• 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.

Answer 1

Answer: (D)

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