There are two springs of spring constants k1 = (20 ± 0.2) N/m and k2 = (30 ± 0.3) N/m. If they are connected in parallel then percentage error in equivalent spring constant of combination is _____%.

The correct answer is 1.

Step-by-step Explanation:

When two springs of spring constants $k_1$ and $k_2$ are connected in parallel, the equivalent spring constant of the combination ($k_{\text{eq}}$) is given by the sum of their individual spring constants:

$k_{\text{eq}}=k_1+k_2$

Given:
$k_1=(20\pm 0.2)\text{N/m}$
Here, the nominal value $k_1=20\text{N/m}$ and the absolute error $\mathrm{��}{k}_1=0.2\text{N/m}$.

$k_2=(30\pm 0.3)\text{N/m}$
Here, the nominal value $k_2=30\text{N/m}$ and the absolute error $\Delta k_2=0.3\text{N/m}$.

Step 1: Calculate the nominal value of the equivalent spring constant ($k_{\text{eq}}$):

$k_{\text{eq}}=20+30=50\text{N/m}$

Step 2: Calculate the absolute error in the equivalent spring constant ($\Delta k_{\text{eq}}$):
For addition, the absolute errors are added directly:

$\Delta k_{\text{eq}}=\Delta k_1+\Delta k_2$

$\Delta k_{\text{eq}}=0.2+0.3=0.5\text{N/m}$

Step 3: Calculate the percentage error in the equivalent spring constant:
The percentage error is given by:

$\text{Percentage Error}=\left(\frac{\Delta k_{\text{eq}}}{k_{\text{eq}}}\right)\times 100\%$

Substituting the values:

$\text{Percentage Error}=\left(\frac{0.5}{50}\right)\times 100\%=1\%$

Thus, the percentage error in the equivalent spring constant of the combination is 1%.