In the given figure velocity of efflux will be:-

In the figure shown, a parallel beam of light is incident on the plane of the slits of a Young's double slit experiment. Light incident on the slit, S₁ passes through a medium of variable refractive index μ = 1 + ax (where 'x' is the distance from the plane of slits as shown), upto a distance 'ℓ' before falling on S₁. Rest of the space is filled with air. If at 'O' a minima is formed, then the minimum value of the positive constant a (in terms of ℓ and wavelength 'λ' in air) is :

A uniform dense rod with non uniform young's modulus is hanging from ceiling under gravity. If elastic energy density at every point is same then young's modulus with x will change as which of the shown graph :-

A vertical U-tube of uniform cross-section contains mercury in both sides of its arms as shown below :

Glycerin column of 20cm is introduced into one of its arms and oil of density 0.8g/cc is poured into other arm until the upper surface of oil and glycerin are at same horizontal level. [ρ_Hg = 13.6 g/cc, ρ_glycerine = 13.6 g/cc] length of oil column is :

A composite rod consists of a steel rod of length ℓ and area 2A and a copper rod of length 2ℓ and area A. The composite rod is subjected to an axial load F. If the Young's modulus of steel and copper are in ratio 2 : 1, then :-

A thin paper of thickness 0.02 mm having refractive index 1.45 is pasted across one of the slit in a Young's double slit experiment. The paper transmits 4/9 of light falling on it. (Wavelength = 600 nm).

A light source, which emits two wavelengths λ₁ = 400 nm and λ₂ = 600 nm, is used in a Young's double slit experiment. If recorded fringe widths for λ₁ and λ₂ are β₁ and β₂ and the number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂, respectively, then :-

Curved surface of a vessel has shape of a truncated cone having semi vertex angle 37°. Vessel is full of water (density ρ = 1000 kg/m³) upto a height of 13 cm and is placed on a smooth horizontal plane. Upper surface is opened to atmosphere. A hole of 1.5 cm² is made on curved wall at a height of 8 cm from bottom as shown in figure. Area of water surface in the vessel is large as compared to the area of hole.

In the front of the upper slit of YDSE apparatus, a thin film of a liquid of refractive index 1.40 is placed. It is a hot day the liquid starts evaporating from the surface. A beam of light at wavelength 560 nm is incident onto the YDSE apparatus and the intensity I at the centre of the screen is monitored. Figure gives intensity I as a function of time t. The intensity changes because of evaporation from the two sides of the film. Assume that the film is flat and has parallel sides. Also assume that the film's thickness decreases at a constant rate.

What can not be the initial thickness of the film?

In the front of the upper slit of YDSE apparatus, a thin film of a liquid of refractive index 1.40 is placed. It is a hot day the liquid starts evaporating from the surface. A beam of light at wavelength 560 nm is incident onto the YDSE apparatus and the intensity I at the centre of the screen is monitored. Figure gives intensity I as a function of time t. The intensity changes because of evaporation from the two sides of the film. Assume that the film is flat and has parallel sides. Also assume that the film's thickness decreases at a constant rate.

If the maximum intensity is I₀, then :-