First slide

Work done by Diff type of forces

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 3k/2.
Reason : The spring connected in series are represented by k = k₁+ k₂. [AIIMS 2017]

Moderate

A

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B

Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C

Assertion is correct but Reason is incorrect.
D

Both Assertion and Reason are incorrect.

Solution

As we know, $k = \frac{F}{l} \Rightarrow k \propto \frac{1}{l}$
$\Rightarrow$ $K_{1} = \frac{1 + 2}{1} K = 3 K a n d K_{2} = \frac{1 + 2}{2} K = \frac{3 K}{2}$

In series, $\frac{1}{k^{'}} = \frac{1}{k_{1}} + \frac{1}{k_{2}} = \frac{1}{3 K} + \frac{2}{3 K} \Rightarrow K^{'} = K$

So, both Assertion and Reason are incorrect.

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