Exams › JEE Main › Physics
A container holding a liquid of density rho is accelerated with acceleration a directed up along an inclined plane of inclination alpha. Find the angle theta that the free surface of the liquid makes with the horizontal.
- tan⁻¹[(a*cos alpha)/(g + a*sin alpha)]
- tan⁻¹[(a + g*sin alpha)/(g*cos alpha)]
- tan⁻¹[a/(g*cos alpha)]
- tan⁻¹[(a - g*sin alpha)/(g(1 - cos alpha))]
Correct answer: tan⁻¹[(a*cos alpha)/(g + a*sin alpha)]
Solution
The acceleration a is along the incline, so its horizontal component is a*cos(alpha) and vertical component is a*sin(alpha) (upward). In the non-inertial frame, pseudo-forces act opposite to acceleration. The free surface tilts so its slope satisfies tan(theta) = a_horizontal / (g + a_vertical) = (a*cos alpha)/(g + a*sin alpha).
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 →