A small sphere of mass M and density $D_{1}$ is dropped in a vessel filled with glycerine. If the density of glycerine is $D_{2}$ then the viscous force acting on the ball will be in Newton.

M D_{1} D_{2}

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

M g [1 - \frac{D_{2}}{D_{1}}]

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

\frac{M D_{1} g}{D_{2}}

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

\frac{M}{g} (D_{1} + D_{2})

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

Open in App

Solution

The correct option is D $M g [1 - \frac{D_{2}}{D_{1}}]$
When sphere is in glycerine, three forces acts on it. which balances each other.
weight $(W)$
buoyant force $(F_{B})$
viscous force $(F_{V})$
and $W = F_{B} + F_{V}$
$\Rightarrow M g = V_{g} D_{2} g + F_{V}$
$\Rightarrow M g = V_{s} D_{2} g + F_{V} ∵ V_{g} = V_{s}$
$\Rightarrow M g = \frac{M}{D_{1}} D_{2} g + F_{V} ∵ V_{s} = \frac{M}{D_{1}}$
$\Rightarrow F_{V} = M g [1 - \frac{D_{2}}{D_{1}}]$

Suggest Corrections

Similar questions

Q. The velocity of small ball of mass

M

and density

d_{1} =

when dropped a container filled with glycerine becomes constant after some time. If the density glycerine is

d_{2}

, the viscous force acting on ball is

Q. A body of density

D_{1}

and mass

M

is moving downward in glycerine of density

D_{2}

. What is the viscous force acting on it?

A body of density $D_{1}$ and mass M is moving downward in glycerin of density $D_{2}$ . What is the viscous force acting on it when it is moving with terminal velocity?

Q. The velocity of a small ball of mass

M

and density

ρ

, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is

\frac{ρ}{2},

then the viscous force acting on the ball will be

A body of density $d_{1}$ is counterpoised by M g of weights of density $d_{2}$ in air of density d. Then the true mass of the body is

Join BYJU'S Learning Program

A small sphere of mass M and density D1 is dropped in a vessel filled with glycerine. If the density of glycerine is D2 then the viscous force acting on the ball will be in Newton.

The correct option is D Mg[1−D2D1]When sphere is in glycerine, three forces acts on it. which balances each other.weight (W)buoyant force (FB)viscous force (FV)and W=FB+FV⇒Mg=VgD2g+FV⇒Mg=VsD2g+FV∵Vg=Vs⇒Mg=MD1D2g+FV∵Vs=MD1⇒FV=Mg[1−D2D1]

A small sphere of mass M and density $D_{1}$ is dropped in a vessel filled with glycerine. If the density of glycerine is $D_{2}$ then the viscous force acting on the ball will be in Newton.