When a ship floats in water, its one fifth volume remains submerged. The maximum weight that can be placed on the ship is 10,000 tons. Calculate the weight the empty ship `(g=10ms^(-2))`.

Explanation

Let the weight of ship be .W. kgf & volume `V m^(3)`. Density of ship `=(W/V)kgfm^(-3)`
Given `(V_(rho))_(g)=(W/V)kgfm^(-3)`
`i.e. rho=rho_(w)/(5)" but"(10^(7)+W)=(V)rho_(w)g`
i.e, `(10^(6)+M)g=vrho_(w)g" where "W=Mg and 10^(7)=10^(6)g`
i.e, `10^(6)+M=(M/p)p_(w)" where "(M/P)=V`
i.e, `10^(6)=M((rho_(w))/(rho)-1)=(M(rho_(w)-p))/(rho)`
`therefore M=(10^(6)rho)/(rho_(w)-rho)=((10^(6)(rho_(w))/(5)))/(rho_(w)-(rho_(v))/(5)) xx (5)/(4rho_(w))`
i.e, `M=0.25 xx 106=250 tons`
Weight of emptly ship=250 ton force.