A spherical solid ball of volume V is made of a material of density -1- It is falling through a liquid of density -1-20- The terminal speed of the ball is

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Floating

A spherical s...

Question

A spherical solid ball of volume $V$ is made of a material of density $ρ_{1}$ . It is falling through a liquid of density $ρ_{1} (ρ_{2} < ρ_{1})$ . Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$ , i.e., $F_{v i s c o u s} = - k v^{2} (k > 0)$ . The terminal speed of the ball is

\sqrt{\frac{V g (ρ_{1} - ρ_{2})}{k}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{V g ρ_{1}}{k}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{\frac{V g ρ_{1}}{k}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{V g (ρ_{1} - ρ_{2})}{k}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\sqrt{\frac{V g (ρ_{1} - ρ_{2})}{k}}$
The condition for terminal speed $(v_{t})$ is
Weight = Buoyant force + Viscous force

$∴ V ρ_{1} g = V ρ_{2} g + k v_{t}^{2}$

$∴ v_{t} = \sqrt{\frac{V g (ρ_{1} - ρ_{2})}{k}}$

Suggest Corrections

Similar questions

Q. A spherical solid ball of volume

V

is made of a material of density

ρ_{1}

. It is falling through a liquid of density

ρ_{1} (ρ_{2} < ρ_{1})

. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed

v

, i.e.,

F_{v i s c o u s} = - k v^{2} (k > 0)

. The terminal speed of the ball is

Q. A spherical solid ball of volume V is made of a material of density

‘ s_{1}

’. It is falling through a liquid of density

‘ s_{2}^{'} (s_{2} < s_{1})

assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed ‘v’,

F_{v i s c o u s} = K \cdot v^{2}

, The terminal speed of the ball is

A spherical solid ball of volume V is made of a material of density $ρ_{1}$ . It is falling through a liquid of density $ρ_{2} (ρ_{2} < ρ_{1})$ . Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., $F_{v i s c o u s} = - k v^{2} (k > 0)$ . The terminal speed of the ball is.

Join BYJU'S Learning Program

The correct option is A √Vg(ρ1−ρ2)kThe condition for terminal speed (vt) is Weight = Buoyant force + Viscous force ∴Vρ1g=Vρ2g+kv2t ∴vt=√Vg(ρ1−ρ2)k

The correct option is A $\sqrt{\frac{V g (ρ_{1} - ρ_{2})}{k}}$
The condition for terminal speed $(v_{t})$ is
Weight = Buoyant force + Viscous force

$∴ V ρ_{1} g = V ρ_{2} g + k v_{t}^{2}$

$∴ v_{t} = \sqrt{\frac{V g (ρ_{1} - ρ_{2})}{k}}$