Exams › JEE Main › Physics
A great many tiny water droplets, each of radius r, coalesce into one larger drop of radius R. If T is the surface tension and J is the mechanical equivalent of heat, find the rise in heat energy per unit volume of the resulting drop.
- 2T/J (1/r - 1/R)
- 2T/(rJ)
- 3T/(rJ)
- 3T/J (1/r - 1/R)
Correct answer: 3T/J (1/r - 1/R)
Solution
Volume conserved: N r³ = R³, so N = (R/r)³. Surface energy released = T(N*4pi r² - 4pi R²) = 4pi T(N r² - R²) = 4pi T(R³/r - R²). Heat per unit volume = released energy / [(4/3)pi R³ * J] = 4pi T(R³/r - R²) / ((4/3)pi R³ J) = 3T(1/r - 1/R)/J.
Related JEE Main Physics questions
- A body is in motion inside a liquid, and the viscous resistive force on it is directly proportional to its speed. What are the dimensions of the proportionality constant?
- A capillary tube has its inner surface lined with wax and is then placed in water. Relative to a clean, unwaxed capillary, how do the contact angle (θ) and the height (h) to which water rises change?
- A charged, isolated spherical soap bubble of radius r has internal pressure equal to atmospheric pressure. If the charge on the bubble is given by Xπ√(2Tε), what is the value of X?
- Two capillary tubes, one of length L and radius R and the other of length 2L and radius 2R, are joined one after the other in series. If the flow rate through a single capillary is X = πPR⁴ / 8ηL, then the combined flow rate through the series arrangement is:
- A liquid will fail to wet the surface of a solid when the angle of contact is
- A gold sphere of a given size falls through a viscous liquid and attains a terminal speed of 0.2 m/s. If the gold has density 19.5 kg/m³ and the liquid has density 1.5 kg/m³, what terminal speed will a silver sphere of the same size have in the same liquid, given that silver has density 10.5 kg/m³?
⚔️ Practice JEE Main Physics free + battle 1v1 →