Answer

Verified

402.3k+ views

**Hint:**If the ball is dipped inside a liquid then the liquid applies a force of buoyancy on the body in the upward direction. The weight of the body will continuously act in the downward direction and the viscous force due to the liquid will act in the opposite direction of the motion of the ball.

**Step by step solution:**

As it is given that the ball is rising up with a constant velocity. If the ball is moving with constant velocity then the value of net force is zero as there is no acceleration to the body.

Let us write the equation of the forces acting on the ball.

As the ball is rising upwards which means that the weight of the body is acting in the downwards direction the viscous force will act in the direction opposite to the direction of the motion of the ball and the buoyancy force will act on the ball upwards. The buoyancy force always acts in the upwards direction, it tries to lift the body up.

The relation of the force is given by,

$ \Rightarrow {F_{net}} = 0$

And the net force is given by,

$ \Rightarrow {\text{weight}} + {\text{viscous force}} = {\text{buoyant force}}$

The weight of the body is equal to,

$ \Rightarrow w = \rho gV$………eq. (1)

The buoyant force is given by,

$ \Rightarrow B = V\left( {4\rho } \right)g$………eq. (2)

Let the viscous force be represented by the term${F_v}$.

The equation will be,

$ \Rightarrow {\text{weight}} + {\text{viscous force}} = {\text{buoyant force}}$

$ \Rightarrow {\text{w}} + {F_v} = B$………eq. (3)

Replace the value of weight and buoyant force in equation (3) from equation (1) and equation (2).

$ \Rightarrow \rho gV + {F_v} = V\left( {4\rho } \right)g$

$ \Rightarrow {F_v} = V\left( {4\rho } \right)g - \rho gV$

$ \Rightarrow {F_v} = 3\rho gV$………eq. (4)

The viscous force is given by${F_v} = 3\rho gV$.

The ratio of viscous force to the weight of the body is given by,

$ \Rightarrow \dfrac{{{F_v}}}{w}$

Replace the value of viscous force and weight from equation (1) and equation (4).

$ \Rightarrow \dfrac{{{F_v}}}{w} = \dfrac{{3\rho gV}}{{\rho gV}}$

After solving the above relation we get,

$ \Rightarrow \dfrac{{{F_v}}}{w} = 3$

So the value of the ratio of viscous force to the weight is equal to 3. So the correct answer

**for this problem is option is option B.**

**Note:**The buoyant force is always in the direction upward direction the weight is always in the downward direction but the viscous force will act in the opposite direction to the motion of the ball as the viscous force will try to stop the motion of the ball

Recently Updated Pages

Draw a labelled diagram of DC motor class 10 physics CBSE

A rod flies with constant velocity past a mark which class 10 physics CBSE

Why are spaceships provided with heat shields class 10 physics CBSE

What is reflection Write the laws of reflection class 10 physics CBSE

What is the magnetic energy density in terms of standard class 10 physics CBSE

Write any two differences between a binocular and a class 10 physics CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE