Question

Two solid spheres of same material but of mass M and 8M, fall simultaneously on a viscous liquid ad their terminal velocities are v and nv, find the value of n

Answer 1

Given that both the solid spheres are of same material, therefore, density of both mass will be same.

For Sphere A, Volume = V, Radius = r.

For Sphere B, Volume = V', Radius = R.

Therefore, Mass/Volume will be same for both the spheres.

M/V = 8M/V'

V' = 8V

R³ = 8r³

R = 2r.

Now, Using the formula of terminal velocity,

Vt = 2/9 r²g(ρ - σ)/η

where, r is the radius of the spheres, η is the coefficient of viscosity, and ρ is the density of spheres and σ is the density of water.

Now, In Both spheres,

2/9, g, (ρ - σ)/η is constant for both the spheres.

∴ Vt ∝ r²

For sphere A,

 v ∝ r² -----(1)

For Sphere B,

 nv ∝ R²

nv ∝ 4r² ---(2).

(1)./(2). ⇒ 1/n = 1/4

∴ n = 4.

Hence, the value of n is 4.

Hope it helps.