A sphere of mass of m = 1.72 kg is first placed directly on the plate of an elec

Question

A sphere of mass of m = 1.72 kg is first placed directly on the plate of an electronic scale. The scale shows 16.87 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of P liquid = 685 kg/m^3 is then placed on the scale and the scale is tared (i.e. zeroed to this weight as a reference point, it has a reading of zero with the beaker on the scale). The sphere, hung by a thin string, is lowered into the liquid and submerges below the surface. (See right figure.) The scale reads 2.79 N with the sphere not touching the beaker. Calculate the density of the sphere.

Explanation / Answer

The mass of sphere m = 1.72 kg

Weight of sphere = 16.87 N

Let the density and volume of sphere be s and Vs respectively.

Density of liquid liq = 685 kg/m3

The reading in the scale after emerging the sphere is due to the gravitational force of the liquid which is displace by the sphere.

Gravitational force = weight of sphere / its mass = 16.87 / 1.72 = 9.808 m/s2

The volume of liquid displaced = volume of the sphere = Vs

Reading on scale 2.79 N = mass of liq. displaced x gravitational force.

2.79 = density of liq. x volume of liq. displaced x 9.808

2.79 = liq. x Vs x 9.808 = 685 x 9.808 x Vs

Vs = 4.153 x 10-4 m3

Volume of sphere Vs 4.153 x 10-4 m3

Density of sphere s = m / Vs = 1.72 / (4.153 x 10-4) = 4141.58 kg/m3

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.