Physics

A long-sighted person (hypermetropic) has difficulty focusing on nearby objects because the image forms behind the retina. A convex lens converges light rays to correct this by focusing the image on the retina.

In a uniform electric field, the forces on the two opposite charges of an electric dipole are equal in magnitude and opposite in direction, resulting in zero net force on the dipole. However, these forces create a torque that tends to align the dipole moment with the electric field. The torque is given by $\vec{\tau }=\vec{p}\times \vec{E}$, where $\vec{p}$ is the dipole moment and $\vec{E}$ is the electric field. Since the net force is zero, the force is not perpendicular or parallel to the dipole moment; rather, there is no net force at all. Therefore, the correct answer is D (None of these).

The displacement vector from point P(1,1,1) to point Q(1,2,2) is calculated as Q - P = (1-1, 2-1, 2-1) = (0, 1, 1). The force vector is given as F = (1, 1, 1). The work done by the force is the dot product of the force vector and the displacement vector: W = F · displacement = (1)(0) + (1)(1) + (1)(1) = 0 + 1 + 1 = 2. Therefore, the correct answer is 2, which corresponds to option B.

The moment (torque) about point P is calculated by the cross product r × F, where r is the position vector from P to Q (1i + 1j + 1k) and F = 2i - j - k. The cross product yields (3j - 3k), which corresponds to option C.

Gamma rays are a form of high-energy electromagnetic radiation emitted during a nuclear explosion and cause significant damage due to their high penetration power and ionizing effects on living tissue. Radio waves and 'Red Waves' do not cause such damage, and 'None of these' is incorrect since gamma rays are the primary damaging radiation.

A steel pin sinks because it displaces less water than its own weight, so the buoyant force is insufficient to keep it afloat. A ship floats because it displaces a volume of water whose weight is equal to or greater than the ship's weight, providing enough buoyant force to support it.

Radio waves are electromagnetic waves and travel at the speed of light, which is much faster than sound waves that travel through air at about 343 m/s. Therefore, radio waves travel faster than sound waves.

In automotive electrical systems, the red wire is conventionally connected to the positive terminal of the car battery to indicate positive voltage and ensure correct polarity.

Energy in a nuclear reaction is produced due to a controlled chain reaction, where the rate of fission is carefully regulated to release energy steadily and safely, such as in nuclear reactors. Control rods and moderators adjust the number of neutrons available to sustain the reaction at a steady rate. An uncontrolled chain reaction leads to an exponential increase in fission events, causing a rapid and potentially destructive release of energy, as seen in nuclear weapons, not sustained energy production.

Thrust in a jet engine is produced when gases are expelled at high speed through a narrow opening (the nozzle), creating a reaction force that propels the engine forward according to Newton's third law of motion.