An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

Options

A. `(4Mg)/(K)`
B. `(2Mg)/(K)`
C. `(Mg)/(K)`
D. `(Mg)/(2K)`

Answer

B

Explanation

Let x be the maximum extension of the spring. When it is loaded with a mass M and released. There is a decrease in the gravitational P.E. and it is = Mgx
But this increases P.E. of the spring
`therefore P.E. =(1)/(2)Kx^(2) " " therefore (1)/(2)Kx^(2)=Mgx " " therefore x = (2Mg)/(K)`