A block of mass m and relative density `y( lt 1)` si attached to an ideal spring of constant K. The system is initially at rest and at equilibrium. If the container acceleration upwards with `a_(0)`, find the increase in the elongation of the spring in equilibrium.

Options

A. `(ma_(0))/(yK)`
B. `(ma_(0))/K(1-y)`
C. `(ma_(0))/K (1/y-1)`
D. `(ma_(0))/K(y-1)`

Answer

C

Explanation

Initially

`rArr V rho g = kx_(0) + mg`…………(i)
Finally

`rArr Vrho (g + a_(0)) = k[x_(0) +x] + m(g + a_(0))`……………..(ii)
(ii) - (ii)
`Vrho a_(0) = kx + ma_(0)`
`x=(ma_(0))/k ((Vrho)/(Vrho_(m)-1))`
`x=(ma_(0))/k (1/lambda-1)`