A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is:
- A
- B
- C
- D
The Correct Option is B
Solution and Explanation
The problem involves understanding the speed-time relationship for a spherical ball dropped in a highly viscous liquid. This is a classic physics problem involving terminal velocity. To determine the correct curve, we need to consider the forces acting on the ball. Initially, gravity accelerates the ball downwards, increasing its speed. As the ball speeds up, viscous drag force, which is proportional to speed in most fluids, opposes this motion.
Formally, the net force \(F\) on the ball can be expressed as:
Net Force: \(F=mg-kv\)
where \(m\) is the mass of the ball, \(g\) the acceleration due to gravity, \(k\) the drag coefficient (a constant for a particular fluid-ball system), and \(v\) the velocity.
As time progresses, the viscous force \(kv\) increases until it balances the gravitational force \(mg\), resulting in a net force of zero. At this point, the ball achieves terminal velocity \(v_t\), where the speed remains constant. Hence:
Terminal Velocity: \(v_t=\frac{mg}{k}\)
The graph of velocity \(v\) versus time \(t\) will show an initial increase in velocity steeply, eventually leveling off as the terminal velocity is achieved. This results in an exponential growth curve that asymptotically approaches \(v_t\).
By comparing graph options, the curve representing this behavior is option B.
Top Questions on mechanical properties of fluid
- A cylindrical pipe has a radius of \( 0.1 \, \text{m} \). If the speed of water flowing through the pipe is \( 2 \, \text{m/s} \), calculate the volume flow rate of water through the pipe.
- MHT CET - 2025
- Physics
- mechanical properties of fluid
- A pipe has a radius of 2 cm at one end and 1 cm at the other end. The velocity of the water at the wider end is 5 m/s. What is the velocity of the water at the narrower end, assuming incompressible flow?
- MHT CET - 2025
- Physics
- mechanical properties of fluid
- A fluid of density \( 800 \, \text{kg/m}^3 \) is flowing through a pipe of varying cross-sectional area. The velocity of the fluid at point A is \( 2 \, \text{m/s} \), and the velocity at point B is \( 4 \, \text{m/s} \). If the cross-sectional area at point A is \( 1 \, \text{m}^2 \), find the cross-sectional area at point B.
- MHT CET - 2025
- Physics
- mechanical properties of fluid
- Water is being poured at the rate of 36 m$^3$/min into a cylindrical vessel whose circular base is of radius 3 meters. Then the water level in the cylinder increases at the rate of:
- MHT CET - 2025
- Physics
- mechanical properties of fluid
- Water flows through a pipe with velocity \( V_1 = 3 \, \text{m/s} \) where the area of the pipe is \( A_1 \). What is the velocity \( V_2 \), where the diameter of the pipe is half of that at area \( A_1 \)?
- KEAM - 2025
- Physics
- mechanical properties of fluid
Questions Asked in NEET exam
- A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contain \(n_1 = 2\) moles and \(n_2 = 3\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :
- NEET (UG) - 2025
- Ideal Gases
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :
- NEET (UG) - 2025
- Moment Of Inertia
The current passing through the battery in the given circuit, is:
- NEET (UG) - 2025
- Current electricity
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
- NEET (UG) - 2025
- Relative Velocity
Concepts Used:
Mechanical Properties of Fluid
The science of the mechanical properties of fluids is called Hydrostatics. A fluid is a substance that relents to the slightest pressure. Fluids are categorized into two classes famed by the names of liquids, and elastic fluids or gases, which later comprehend the air of the atmosphere and all the different kinds of air with which chemistry makes us acquainted.
Streamline Flow:
A streamline is a curve the tangent to which at any point provides the direction of the fluid velocity at that point. It is comparable to a line of force in an electric or magnetic field. In steady flow, the pattern of the streamline is motionless or static with time, and therefore, a streamline provides the actual path of a fluid particle.
Tube of Flow:
A tubular region of fluid enclosed by a boundary comprises streamlines is called a tube of flow. Fluid can never cross the boundaries of a tube of flow and therefore, a tube of flow acts as a pipe of the same shape.
Surface Tension and Viscosity:
The surface tension of a liquid is all the time a function of the solid or fluid with which the liquid is in contact. If a value for surface tension is provided in a table for oil, water, mercury, or whatever, and the contacting fluid is unspecified, it is safe to consider that the contacting fluid is air.