Exams › JEE Main › Physics
In a sprayer, air of density rhoₐ moves over the top of a liquid (density rhoₗ) tube. For a fixed piston (air) speed, the volume of liquid sprayed per unit time is proportional to which of the following?
- sqrt(rhoₐ/rhoₗ)
- sqrt(rhoₗ/rhoₐ)
- sqrt(rhoₐ*rhoₗ)
- rhoₗ
Correct answer: sqrt(rhoₐ/rhoₗ)
Solution
The pressure reduction created by the air stream is proportional to rhoₐ*v². This drop drives the liquid out; equating it to the liquid's kinetic energy term (1/2)*rhoₗ*u² gives u proportional to sqrt(rhoₐ/rhoₗ)*v. The volume flow rate (area times u) is therefore proportional to sqrt(rhoₐ/rhoₗ).
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 →