The diagrams show a metal cube suspended from a spring balance before and during immersion in water.

Question 35

The diagrams show a metal cube suspended from a spring balance before and during immersion in water.

A reduction in the balance reading occurs as a consequence of the immersion.

Which statement is correct?

A The balance reading will be further reduced if the cube is lowered further into the water.

B The balance reading during immersion corresponds to the upthrust of the water on the cube.

C The forces acting on the vertical sides of the cube contribute to the change in the balance reading.

D The gravitational pull on the cube is unchanged by the immersion.

Reference: Past Exam Paper – November 2010 Paper 12 Q13

Solution:

Answer: D.

Before the immersion, the balance reads the weight of the object, which is downwards. The weight of the cube is the gravitational pull on the cube and this is unchanged in a specific location since weight W = mg. [D is correct]

As the cube is immersed, it experiences an upthrust force upwards. This force is due to the difference in pressures acting on the top and bottom of the cube.

Pressure = hρg

The pressure on the bottom face of the cube is greater than the pressure at the top face. This is because the lower face is at a greater depth in the water.

Pressure = Δhρg

where Δh is the difference in depth of the top and bottom faces.

It is be noted that Δh is also the length of the cube.

For whatever depth of immersion of the cube, the pressure is given by P = Δhρg. Since the length of the cube does not change (Δh is constant), the upthrust force on the cube will always have the same value at any depth when fully immersed. Thus, the upthrust is unchanged no matter how further the cube is immersed. [A is incorrect]

The forces acting on the vertical sides of the cube are equal in magnitude since they act at the same depth in the water. So, they cancel each other out and are not the cause in the change in the balance reading. [C is incorrect] The balance reading is affected by the vertical forces acting on the cube (weight and upthrust).

Thus, the balance reading is not the upthrust but the weight (which acts downwards) minus the upthrust (which acts upwards). The balance reads the resultant of these two forces. [B is incorrect]