Question

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is B

To resolve this, we must examine the movement of a small steel sphere descending into a viscous medium such as glycerine.

Upon release, the steel sphere initially accelerates under gravity. However, as it penetrates the glycerine, it encounters an opposing viscous drag force, the magnitude of which escalates with its speed. Consequently, the sphere attains a constant speed, termed terminal velocity, at which point the resultant force acting upon it is null.

The forces influencing the sphere are:

1. Gravitational force \(mg\) (directed downwards)
2. Buoyant force \(F_B\) (directed upwards, exerted by the glycerine)
3. Viscous drag force \(F_d\) (directed upwards, proportional to velocity)

These forces equilibrate, leading the sphere to achieve its terminal velocity \(v_t\).

The velocity-time graph for this phenomenon will exhibit:

• An initial accelerating gradient as the sphere's velocity increases due to gravity.
• Subsequently, it will transition to a horizontal segment once terminal velocity is attained, denoting uniform velocity.

The accurate graphical representation depicts an initial steep gradient that progressively flattens to a constant value, aligning with the accompanying image:

Therefore, the correct depiction is the option illustrated by the image, where velocity initially rises and subsequently stabilizes upon reaching terminal velocity.