A block of mass m falls from a height h onto the end of a platform as shown in figure. The springis initially unstreched and the mass of the platform on be neglected. Assuming if there is no loss of energy, the maximum elongation of the spring is

Options

A. `(mg+sqrt(m^(2)g^(2)+2mghK))/(K)`
B. `(mg+sqrt(m^(2)g^(2)-2mghk))/(K)`
C. `(K)/sqrt(m^(2)g^(2)+2mghk)`
D. `sqrt(m^(2)g^(2)+2mghk)/(K)`

Explanation

Let x be the elongation produced in string mg
`(h+x)=(1)/(2)kx^(2)`
`x=mg+sqrt(m^(2)g^(2)+2mghk)`
K