A ball of mass 2kg is moving with velocity 3m/s,collides with spring of natural length 2m and force constant 144 N/m. What will be length of compressed spring?
1. 2m
2. 1.5m
3. 1m
4. 0.5m

Asked by Mamali Nanda | 14th Jul, 2016, 09:23: PM

Expert Answer:

begin mathsize 12px style Energy space of space the space spring space and space ball space system space is space conserved.
Let space us space assume space that space the space spring space is space compressed space by space straight a space length space say space apostrophe straight x apostrophe.
We space have comma
1 half mv squared equals 1 half kx squared space
where space straight k space is space the space spring space constant.
Given space that space straight m equals 2 space kg comma space straight v equals 3 space straight m divided by straight s space and space straight k equals 144 space straight N divided by straight m
1 half cross times 2 cross times left parenthesis 3 right parenthesis squared equals 1 half cross times 144 cross times straight x squared
9 equals 72 straight x squared
rightwards arrow straight x equals fraction numerator 1 over denominator 2 square root of 2 end fraction straight m
Given space that space the space natural space length space of space the space spring space is space 2 straight m.
Thus comma space length space of space the space compressed space spring space is space 2 space minus space fraction numerator 1 over denominator 2 square root of 2 end fraction
rightwards arrow space equals space 1.65 space straight m

bold Note colon space The space answer space does space not space match space with space the space given space options.
space end style

Answered by Yashvanti Jain | 15th Jul, 2016, 11:15: AM