Work Energy Power

JEE Main level, numerical answer, medium

101 of 183

Question 101 of 183

A ball of mass 4kg4kg, moving with a velocity of 10ms−110{ms}^{-1}, collides with a spring of length 8m8m and force constant 100Nm−1100N{m}^{-1}. The length of the compressed spring is xmxm. The value of xx, to the nearest integer, is ___ .

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Answer: 6

Let's say the compression in the spring by:yy. So, by work-energy theorem we have
⇒12mv2=12ky2\Rightarrow \dfrac{1}{2}m{v}^{2}=\dfrac{1}{2}k{y}^{2}⇒y=mk⋅v\Rightarrow y=\sqrt{\dfrac{m}{k}}\cdot v⇒y=4100×10\Rightarrow y=\sqrt{\dfrac{4}{100}}\times 10⇒y=2m\Rightarrow y=2m
⇒\Rightarrow Final length of spring,=8−2=6m=8-2=6m.

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