Question

In air, a metallic sphere with an internal cavity weighs 40g and in water it weighs 20g. The volume of cavity if the density of material with cavity be 8g/cm${}^3$ is:

• A. zero
• B. 15 cm${}^3$
• C. 5 cm${}^3$
• D. 20 cm${}^3$

Answer 1

Answer: (B)

15 cm${}^3$

Neglecting the upthrust in air,
Mass of metallic sphere = 40 gms
Density of Material=$8g/c{m}^3$
So,
Volume of the metal used = $5c{m}^3$-------(1)
When dipped in water,
Loss in weight = $20$ g
So, Volume of water displaced/volume of sphere= $20c{m}^3$-----------(2)
From (1) and (2),
Volume of cavity =$(20-5)c{m}^3$
=$15c{m}^3$