Question

5. A block of silver displaces 200 mL of water in a measuring cylinder. If the density of silver is 10300 kg m-3, find the mass of block. ​

Answer 1

Answer:

According to Archimedes principle,

Buoyant Force = - (pV)g

where, pV is mass of the object immersed in the liquid, 'p' is the density of the object, 'V' is the volume displaced by the object.

Hence we can say that, mass of the object is:

⇒ m = pV ...(i)

Now we are given that, density of the object is 10300 kg/m³ and volume of the liquid displaced is 200 ml. Since the density has the volume in terms of m³, we convert volume from ml to m³. Hence we get:

⇒ 1 ml = 10⁻⁶ m³ :: 200 ml = ? (x)

⇒ x = 200 × 10⁻⁶

⇒ x = 2 × 10⁻⁴ m³

Substituting the information in (i) we get:

⇒ m = 10300 kg/m³ × 2 × 10⁻⁴ m³

⇒ m = 1.03 × 2 × 10⁴ × 10⁻⁴

⇒ m = 2.06 kg

Hence the mass of the silver block is 2.06 kg