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(D) According to the law of conservation of mechanical energy,the potential energy at the initial height is converted into the elastic potential energ

Vedclass · Accepted Answer

$9.8$

Vedclass · Answer

(D) According to the law of conservation of mechanical energy,the potential energy at the initial height is converted into the elastic potential energy of the spring at maximum compression.$mgh = \frac{1}{2} kx^2$Given:Mass $m = 40 \ g = 0.04 \ kg$Height $h = 4.9 \ m$Spring constant $k = 400 \ N/m$Acceleration due to gravity $g = 9.8 \ m/s^2$Substituting the values:$0.04 	imes 9.8 	imes 4.9 = \frac{1}{2} 	imes 400 	imes x^2$$1.9208 = 200 	imes x^2$$x^2 = \frac{1.9208}{200} = 0.009604$$x = \sqrt{0.009604} = 0.098 \ m$Converting to centimeters: $x = 0.098 	imes 100 = 9.8 \ cm$.

$A$ smooth track extends to a horizontal part as shown in the figure. $A$ spring with a force constant of $400 \ N/m$ is firmly attached to one end of this horizontal part. $A$ mass of $40 \ g$ is released from a height of $4.9 \ m$. Calculate the compression in the spring in $cm$.

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