Physics

The Venturi relation describes the pressure difference between two points in a fluid flow when the velocity changes, given by the formula P1 - P2 = 1/2 ρ (V2² - V1²). This is derived from Bernoulli's principle and the continuity equation. Option A is the closest to the correct Venturi relation, although it omits the V1² term explicitly, which is essential for the full expression. The other options represent different fluid dynamics equations unrelated to the Venturi relation.

The speed of efflux of a fluid from an orifice can be determined using Torricelli's theorem, which relates the speed to the height of the fluid column. Bernoulli's theorem is a more general principle from which Torricelli's theorem can be derived, but Torricelli's theorem specifically addresses efflux speed. The 'Venture relation' is not relevant here, and 'All' is incorrect because not all options apply.

Electric charge is a derived quantity in the SI system because it is defined in terms of the base unit electric current (ampere) multiplied by time (second). Electric current, plane angle, and amount of substance are base quantities or dimensionless quantities.

The rotational kinetic energy of a rotating object is given by K.E = (1/2) I ω², where I is the moment of inertia and ω is the angular velocity. For a hoop, the moment of inertia about its central axis is I_hoop = MR². For a solid disc, the moment of inertia is I_disc = (1/2) MR². Given the same mass, radius, and angular velocity, the hoop's rotational kinetic energy is K.E_hoop = (1/2)(MR²)ω² = (1/2)MR²ω², while the disc's rotational kinetic energy is K.E_disc = (1/2)((1/2)MR²)ω² = (1/4)MR²ω². Therefore, K.E_hoop = 2 × K.E_disc. Hence, the hoop has twice the rotational kinetic energy of the disc when both rotate at the same angular velocity.

Laminar flow typically occurs at low flow speeds where the fluid moves in smooth, orderly layers without turbulence. At higher speeds, flow tends to become turbulent.

For small droplets falling through air, the terminal velocity is proportional to the square of the radius of the droplet. Given the radii ratio of 2:3, the terminal velocity ratio is (2^2):(3^2) = 4:9. Among the options, '4:09' (option B) correctly represents this ratio. The original answer '4:06' (option A) is incorrect and likely a typographical error.

Fundamental science is often considered to have two main frontiers: the frontier of the very large (cosmology, astrophysics) and the frontier of the very small (particle physics, quantum mechanics). Therefore, the correct answer is 2.

In simple harmonic motion, the total energy of the system is proportional to the square of the amplitude because energy depends on both kinetic and potential energy, which are proportional to the square of displacement (amplitude).

A geostationary satellite orbits the Earth once every 24 hours, matching the Earth's rotation period, which allows it to remain fixed over one position on the equator.

At the highest point in vertical circular motion, the tension in the string is less than the weight of the stone because the weight provides part of the centripetal force needed to keep the stone moving in a circle. The tension is not zero unless the stone is just about to lose contact, and it is not equal to or maximum compared to the weight at the top position.