If the system is suspended by the mass m the length of the spring is `l_(1)`. If it is inverted and hung by mass M, the length of the spring is `l_(2)`. Find the natural length of the spring.

Options

A. `(ml_(1)+Ml_(2))/(m+M)`
B. `(ml_(2)+Ml_(1))/(m+M)`
C. `(ml_(1)-Ml_(2))/(m-M)`
D. `(ml_(2)-Ml_(1))/(m-M)`

Answer

C

Explanation

`k(l_(1)-l_(0))=Mg`
`k(l_(2)-l_(0))=mg`
`(l_(1)-l_(0))/(l_(2)-l_(0))=M/m`
`ml_(1)-ml_(0) =Ml_(2)-Ml_(0)`
`l_(0)=(ml_(1)-Ml_(2))/(m-M)`