A ball of mass 4, kg,moving with a velocity o | vedclass

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(C) According to the law of conservation of mechanical energy,the kinetic energy of the ball is converted into the potential energy of the spring at t

Vedclass · Accepted Answer

$6$

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(C) According to the law of conservation of mechanical energy,the kinetic energy of the ball is converted into the potential energy of the spring at the point of maximum compression.Let the compression in the spring be $y$.By the work-energy theorem or conservation of energy:$\frac{1}{2} mv^2 = \frac{1}{2} ky^2$Substituting the given values: $m = 4\, kg$,$v = 10\, ms^{-1}$,$k = 100\, Nm^{-1}$.$\frac{1}{2} 	imes 4 	imes (10)^2 = \frac{1}{2} 	imes 100 	imes y^2$$2 	imes 100 = 50 	imes y^2$$200 = 50 	imes y^2$$y^2 = 4$$y = 2\, m$The initial length of the spring is $8\, m$. The compressed length $x$ is given by:$x = 	ext{Initial length} - 	ext{Compression}$$x = 8 - 2 = 6\, m$.Thus,the value of $x$ is $6$.

$A$ ball of mass $4\, kg$,moving with a velocity of $10\, ms^{-1}$,collides with a spring of length $8\, m$ and force constant $100\, Nm^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$,to the nearest integer,is ........ .

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