First slide

Potential energy

Question

A block of mass 2 kg is dropped from a height of 40 cm on a spring whose force-constant is 1960 N $m^{- 1}$ . The maximum distance through which the spring is compressed by

Easy

A

5 cm
B

15 cm
C

20 cm
D

10 cm

Solution

$mg (h + x) = \frac{1}{2} {kx}^{2}$
Here, $m = 2 kg, h = 40 cm$
$k = 1960 {Nm}^{- 1} and g = 10 {ms}^{- 2}$
$∴ 2 \times 10 (0.4 + x) = \frac{1}{2} \times 1960 x^{2}$
$8 + 20 X = 980 X^{2}$
On solving, we get x = 10 cm.

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