Question

A floating raft of mass 500 kg has 8 cm of its
thickness submerged inside water. If a body of
mass m is placed on the raft, then submerged part
changes to 9 cm. The mass of the body (m) is
(1) 125 kg
(2) 62.5 kg
(3) 80 kg
(4) 75.5 kg
​

Answer 1

Answer:

(2). The mass of the body is 62.5 kg.

Explanation:

Given that,

Mass m = 500 kg

Distance h= 8 cm

Weight of the body = buoyant force

$mg=\rho gh$

Here, m = mass

$\rho$ = density

h = height,

$500g=\rho\ g\times 8$....(I)

If a body of  mass m is placed on the raft, then submerged part  changes to 9 cm.

Therefore,

$(500+m)g=\rho\ g\times 9$....(II)

on dividing equation (I) by equation (II)

$\dfrac{500g}{(500+m)g}=\dfrac{\rho\ g\times 8}{\rho\ g\times 9}$

$4500=4000+8m$

$m =\dfrca{500}{8}$

$m = 62.5 kg$

Hence, The mass of the body is 62.5 kg.