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Variation of G Due to the Rotation of Earth

A block of 2 ...

Question

A block of 2 kg is suspended from the ceiling through a massless spring of spring constant k = 100 N/m. What is the elongation of the spring ? If another 1 kg is added to the block, what would be the further elongation ?

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Solution

Given, m = 2k , k = 100 N/m

From the free body diagram...

kl - 2g = 0

$\Rightarrow k l = 2 g$

$\Rightarrow l = \frac{2 g}{k} = \frac{2 \times 9.8}{100}$

= $\frac{19.6}{100} = 0.196 \approx 0.2 m$

Suppose further elongation happens when 1 kg block us added be x.

Then k (l + x ) = 3g

$\Rightarrow k x = 3 g - 2 g = g = 9.8 N$

$\Rightarrow \frac{2 g}{k} = \frac{2 \times 9.8}{100}$

= $\frac{19.6}{100} = 0.098 = 0.1 m$

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