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  • A ball of mass 4kg moving with a velocity of 10 ms-1 , collides with a spring of length 8m and force constant 100 Nm-1. The length of the compressed spring is x m. The value of x, to the nearest interger is _______ <st

A ball of mass 4kg moving with a velocity of 10 ms-1 , collides with a spring of length 8m and force constant 100 Nm-1. The length of the compressed spring is x m. The value of x, to the nearest interger is _______
Option: 1 6
Option: 2 2
Option: 3 8
Option: 4 10

Answers (1)

best_answer

\text{Let's say the compression in the spring by : $y$.} \\ \\ \text{So, by work energy theorem we have}

\begin{array}{l} \Rightarrow \frac{1}{2} mv ^{2}=\frac{1}{2} ky ^{2} \\ \\ \Rightarrow y =\sqrt{\frac{ m }{ k }} \cdot v \\ \\ \Rightarrow y =\sqrt{\frac{4}{100}} \times 10 \\\\ \Rightarrow y =2 m \end{array}

\begin{aligned} &\Rightarrow \text { final length of spring }\\ &=8-2=6 m \end{aligned}

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Deependra Verma

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