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Standard XII

Physics

Spring Block's Time Period

A block of ma...

Question

A block of mass $1 k g$ falls from a height of $5 m$ on a vertical spring fastened to a horizontal board placed on the floor. If the spring constant of the spring is $10 N / m$ , the maximum compression that the spring undergoes is:

1.7 m

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3.4 m

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4.3 m

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0.43 m

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Solution

The correct option is C $4.3 m$
By energy conservation,
$\frac{1}{2} k x^{2} = m g (5 + x)$
$5 x^{2} = 50 + 10 x$
$x^{2} - 2 x - 10 = 0$
$x = \frac{2 \pm \sqrt{4 + 40}}{2}$
$x = \frac{2 \pm \sqrt{44}}{2}$
$= 3 \pm \sqrt{11}$
$x = 4.3 m$

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A block of mass 1 kg falls from a height of 5 m on a vertical spring fastened to a horizontal board placed on the floor. If the spring constant of the spring is 10 N/m, the maximum compression that the spring undergoes is:

The correct option is C 4.3 mBy energy conservation,12kx2=mg(5+x)5x2=50+10xx2−2x−10=0x=2±√4+402x=2±√442=3±√11x=4.3m

A block of mass $1 k g$ falls from a height of $5 m$ on a vertical spring fastened to a horizontal board placed on the floor. If the spring constant of the spring is $10 N / m$ , the maximum compression that the spring undergoes is:

The correct option is C $4.3 m$
By energy conservation,
$\frac{1}{2} k x^{2} = m g (5 + x)$
$5 x^{2} = 50 + 10 x$
$x^{2} - 2 x - 10 = 0$
$x = \frac{2 \pm \sqrt{4 + 40}}{2}$
$x = \frac{2 \pm \sqrt{44}}{2}$
$= 3 \pm \sqrt{11}$
$x = 4.3 m$