A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given \(\pi\) = 3.14)
(Given \(\pi\) = 3.14)
\(8.5 × 10^{–4} J\)
\(8.2 × 10^{–4} J\)
\(7.5 × 10^{–4} J\)
\(5.3 × 10^{–4} J\)
The Correct Option is C
Solution and Explanation
\(729×\frac 43\pi r^3=\frac 43\pi R^3\)
\(R = 9r\) ……(1)
Then, the gain in surface energy
\(ΔU = S × ΔA\) …..(2)
\(△U=S×{−4\pi R^2+729×4\pi r^2}\)
\(△U=S×4π(729r^2–81r^2)\)
\(△U=7.5×10^{−4}J\)
So, the correct option is (C): \(7.5 × 10^{–4} J\)
Top Questions on kinetic theory
- The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where \( R \) is the gas constant, \( T \) is the temperature, and \( M_0 \) is the molecular mass. If the temperature is increased, find the new RMS velocity \( v_{\text{rms}} \) when the temperature is doubled.}
- MHT CET - 2025
- Physics
- kinetic theory
- A cubical box of side 1 m contains Boron gas at a pressure of 100 Nm$^{-2}$. During an observation time of 1 second, an atom travelling with the rms speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. The total mass of gas in the box in gram is:
- COMEDK UGET - 2024
- Physics
- kinetic theory
Consider a rope fixed at both ends under tension so that it is horizontal (i.e. assume the rope is along x-axis, with gravity acting along z-axis). Now the right end is continually oscillated at high frequency n (say n=100 Hz) horizontally and in a direction along the rope; amplitude of oscillation is negligible. The oscillation travells along the rope and is reflected at the left end.
Let the total length of rope be l, total mass be m and the acceleration due to gravity be g.
After initial phase (say a mintue or so), the rope has __(BLANK-1)__ wave, which is __(BLANK-2)__ in nature. It results from superposition of left travelling and right travelling __(BLANK-3)__ waves. This resulting wave has a frequency __ (BLANK-4)_ that of oscillation frequency nu. Simple dimensional analysis indicates that the frequency of can be of the form: ___(BLANK-5)__ .- IIITH UGEE - 2024
- Physics
- kinetic theory
- At which temperature will the r.m.s. velocity of a hydrogen molecule be equal to that of an oxygen molecule at \( 47^\circ \text{C} \)?
- MHT CET - 2024
- Physics
- kinetic theory
- If \( n \) is the number density and \( d \) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e., mean free path) is represented by:
- MHT CET - 2024
- Physics
- kinetic theory
Questions Asked in JEE Main exam
- The number of non-empty equivalence relations on the set \(\{1,2,3\}\) is :
- JEE Main - 2025
- Set Theory
- The sum of the squares of all the roots of the equation \( x^2 + [2x - 3] - 4 = 0 \) is:
- JEE Main - 2025
- Quadratic Equations
- Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
- JEE Main - 2025
- Trigonometry
- The spin-only magnetic moment (\(\mu\)) value (B.M.) of the compound with the strongest oxidising power among \(Mn_2O_3\), \(TiO\), and \(VO\) is ________________________ B.M. (Nearest integer).
- JEE Main - 2025
- Magnetic moment
- Atomic number of element with lowest first ionisation enthalpy is:
- JEE Main - 2025
- Periodic Table
Concepts Used:
Kinetic Theory
The kinetic theory is a fundamental concept in physics and chemistry that describes the behavior of gases, liquids, and solids in terms of the motion of their constituent particles. According to the kinetic theory, all matter is made up of tiny particles, such as atoms or molecules, that are constantly in motion.
The kinetic theory postulates that the temperature of a substance is directly proportional to the average kinetic energy of its particles. The higher the temperature, the greater the motion of the particles, and the more energy they possess.
In a gas, the kinetic theory explains that the particles move randomly and independently, colliding with one another and with the walls of their container. These collisions are elastic which means that no energy has lost during the collision. As a result, the pressure of the gas is directly related to the average speed of its particles and the number of collisions per unit area.
In a liquid or a solid, the particles are more closely packed and have less freedom of motion than in a gas. However, they still vibrate and move, and the kinetic theory explains their behavior in terms of the strength of their intermolecular forces and the amount of energy they possess.
Overall, the kinetic theory provides a framework for understanding the behavior of matter at the atomic and molecular level and has many practical applications, such as in the design of engines, the production of gases, and the study of the properties of materials.