A solid, homogeneous sphere with a mass of m_0, a radius of r_0 and a density of

Question

A solid, homogeneous sphere with a mass of m_0, a radius of r_0 and a density of rho_0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'r or f or s' are possible answers in some of the cases. The new sphere has a mass of m > m_0 and a density of rho

Explanation / Answer

1. for given sphere,

weight force = buoyancy force

m0 g = V_submerged * rho_water * g

m0 = v_submerged rho_water ..... (i)

and m0 = rho0 k r0^3

where k = 4 pi / 3

k rho0 r0^3 = v_submerged rho_water .... (ii)

1. m > m0 hence v_submerged will increase.

Ans: r

2. m < m0

v_submerged will decrease.

Ans: f

3. r < r0, rho > rho0

so rho r^3 may decrease Or increase Or may stay same depends on values by which they change.

Ans: r , f , s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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