Log of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink, should be (density of wood =600 kg m) (1) 80 kg (2) 50 kg (3) 60 kg (4) 30 kg
Answers
The weight that can be put on the raft to make it just sink, should be
(1) 80 kg
When an object of mass 'm' kg is put on the raft, it makes it sink. Before that the log of wood floats on water.
Let the volume of the raft be 'V'.
We know, volume = (mass / density). So,
Vol. of raft = (mass of raft)/(density of raft)
= 120kg/600kg m⁻³ [As mass and density of wood is provided in question.]
= 0.2 m³ .
From Archimedes' Principle, after the addition of the extra mass, the buoyancy provided by water must balance the weight of raft and the extra mass.
Combined mass = (120+m) kg
Thus,
Mass of water × Acc. due to gravity = Combined mass × Acc. due to gravity
[As the forces are equal and Force = Mass × Acceleration.]
⇒ 1000 × 0.2 × g = (120 + m) × g [Mass = Density × Volume and Density of water is 1000kg m⁻³ and g is the acceleration due to gravity.]
⇒ 120 + m = 200
⇒ m = 200 - 120 = 80
So, mass is 80kg and option (1) is correct.