JEE Physics 2025 Question with Solution

Given: A spherical ball of mass $M$ falls through glycerine and attains terminal velocity. The density of glycerine is half the density of the ball.

Find: The viscous force acting on the ball at terminal velocity.

At terminal velocity, the net force on the ball is zero. The forces acting are:

• Weight $Mg$ downward
• Buoyant force $F_b$ upward
• Viscous force $F_v$ upward

So the force balance is

Let the density of the ball be $\rho_b$ and the density of glycerine be $\rho_f$. Then

and the buoyant force is

Hence,

so

Given

therefore

Using $M = V\rho_b$,

Therefore, the viscous force acting on the ball is $\frac{Mg}{2}$. This corresponds to option C.

The solution also shows option B, but the force balance including buoyancy gives $\frac{Mg}{2}$, so there is a discrepancy in the source solution.

The first approach on the solution states that at terminal velocity the viscous drag equals the weight of the ball, that is,

but this ignores the buoyant force exerted by glycerine.

For a body moving in a fluid, terminal velocity means total upward force equals total downward force, not drag alone equals weight. Thus,

not

Since the fluid density is half the ball density,

Therefore,

So the physically correct answer is option C, even though the source marks B.