Potential Energy = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.

The swimmer's speed relative to the bank when swimming upstream is 3 m/s - 1 m/s = 2 m/s.

Using τ = Iα, we have α = τ/I = 10 N·m / 2 kg·m² = 5 rad/s².

Using the formula ω = ω₀ + αt, where ω₀ = 0, α = 2 rad/s², and t = 5 s, we get ω = 0 + 2 * 5 = 10 rad/s.

If the angular velocity is constant, the angular acceleration is zero.

The acceleration due to gravity near the Earth's surface is approximately 9.8 m/s².

The acceleration due to gravity near the Earth's surface is approximately 9.81 m/s².

In free fall, the only force acting on the object is its weight, which is the net force.

An object moving in a circular path experiences centripetal acceleration directed towards the center of the circle.

If the magnetic field strength is doubled, the induced emf also doubles, as it is directly proportional to the magnetic field strength.

According to Lenz's law, the induced current will flow in a direction that opposes the change in magnetic flux. If the magnetic field is increasing, the induced current will be counterclockwise.

The frequency f is inversely proportional to the square root of the mass m, so if m is tripled, the frequency is reduced to one-third.

Centripetal force is given by F = mv^2/r. If r is doubled, the force is halved, assuming mass and velocity remain constant.

Centripetal force F = mv²/r; if r is doubled, F is halved for constant speed.

The period T is inversely proportional to the square root of the spring constant k. If k is doubled, the period is halved.

The total momentum of the system before the collision is the vector sum of the momenta of the two particles, which is m1 * v1 + m2 * v2.

The interference pattern is caused by the superposition of light waves from the two slits.

Acceleration a = F/m = 16 N / 4 kg = 4 m/s².

In a perfectly inelastic collision, the two colliding objects stick together, and some kinetic energy is transformed into other forms of energy, resulting in a loss of kinetic energy.

For stability in rolling motion, the center of mass must be above the base to ensure that the object does not tip over.

If the total external torque acting on a system of particles is zero, the angular momentum of the system remains constant according to the conservation of angular momentum.

This describes an elastic collision, where both momentum and kinetic energy are conserved.

According to Newton's third law, for every action, there is an equal and opposite reaction, meaning the reaction force is equal and opposite to the applied force.

The average kinetic energy of gas molecules is directly proportional to the absolute temperature.

Flux linkage refers to the total magnetic flux through a coil, which is the product of the magnetic flux and the number of turns in the coil.

The moment of inertia depends on both the mass distribution and the shape of the object relative to the axis of rotation.

The moment of inertia I of a point mass m at a distance r from the axis of rotation is given by I = m * r^2.

The moment of inertia is the rotational analog of mass, representing how difficult it is to change the rotational motion of an object.

The maximum displacement from the equilibrium position in simple harmonic motion is called the amplitude.

At maximum displacement, the potential energy is at its maximum while kinetic energy is zero.