Question
Tue March 24, 2015 By: R K Jha

A body of mass 120 kg and density 600kg/m3 floats in water. The additional mass to be added to the body so that the body does not sink is:

(a)20 kg   (b) 80 kg    (c)100kg      (d)120 kg

Expert Reply
Yashvanti Jain
Tue March 24, 2015
Correct option (a) 20 kg
Let 'm' be the maximum mass that can to be added to the body such that the body does not sink:
We know that:
Weight of the water displaced = Weight of body + Maximum mass that can be added
begin mathsize 14px style straight rho subscript straight W Vg space equals Mg straight i. straight e space straight rho subscript straight W straight V space equals straight M Or comma space straight rho subscript straight W straight V space equals left parenthesis 120 space plus space straight m right parenthesis straight rho subscript straight W space equals space 1000 space kg divided by straight m cubed straight V space equals space 120 over 600 space equals 0. space 2 space straight m cubed Substitutingthe space values space we space get colon 1000 space cross times 0. space 2 space equals space 120 space plus space straight m straight m space equals space 200 space minus space 120 space equals space 80 space kg end style
So, if 80 kg mass or above this is added to the body, it will sink. Hence on adding 20 kg mass the body will float.
 
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