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Standard XII

Physics

Spring Force

A block of 4 ...

Question

A block of $4 k g$ is suspended from the ceiling through a massless spring of spring constant $k = 100 N / m$ . If $4 k g$ is replaced by $8 k g$ , what would be the ratio of elongation in 1st case to 2nd case?

1

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0.5

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Solution

The correct option is D $0.5$
FBD of the block,

For equilibrium, spring force = Weight of the block
Case (1)
$k x_{1} = m_{1} g \Rightarrow x_{1} = \frac{m_{1} g}{k} \Rightarrow \frac{4 (10)}{100} = 0.4 m$
Case (2)
$x_{2} = \frac{m_{2} g}{k} = \frac{8 (10)}{100} = 0.8 m$

Ratio $= \frac{0.4}{0.8} = 0.5$

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A block of 4 kg is suspended from the ceiling through a massless spring of spring constant k=100 N/m. If 4 kg is replaced by 8 kg, what would be the ratio of elongation in 1st case to 2nd case?

The correct option is D 0.5FBD of the block, For equilibrium, spring force = Weight of the block Case (1) kx1=m1g⇒x1=m1gk⇒4(10)100=0.4 m Case (2) x2=m2gk=8(10)100=0.8 m Ratio =0.40.8=0.5

A block of $4 k g$ is suspended from the ceiling through a massless spring of spring constant $k = 100 N / m$ . If $4 k g$ is replaced by $8 k g$ , what would be the ratio of elongation in 1st case to 2nd case?