A ball of mass 4   kg , moving with a velocity of 10   m   s - 1 , collides with a spring of length 8   m and force constant 100   N   m - 1 . The length of the compressed spring is x   m . The value of x , to the nearest integer, is ___ .

Question

A ball of mass 4 &#160; kg , moving with a velocity of 10 &#160; m &#160; s - 1 , collides with a spring of length 8 &#160; m and force constant 100 &#160; N &#160; m - 1 . The length of the compressed spring is x &#160; m . The value of x , to the nearest integer, is ___ .

Aicharya · Accepted Answer

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

$\Rightarrow \frac{1}{2} m v^{2} = \frac{1}{2} k y^{2}$ $\Rightarrow y = \sqrt{\frac{m}{k}} \cdot v$ $\Rightarrow y = \sqrt{\frac{4}{100}} \times 10$ $\Rightarrow y = 2 m$

$\Rightarrow$ Final length of spring, $= 8 - 2 = 6 m$ .

A ball of mass 4   kg , moving with a velocity of 10   m   s - 1 , collides with a spring of…

Solution

A ball of mass 4 &#160; kg , moving with a velocity of 10 &#160; m &#160; s - 1 , collides with a spring of…

Solution

A ball of mass 4 kg , moving with a velocity of 10 m s - 1 , collides with a spring of…