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\(M_{bullet}\) = 0.05kg, \(V_{bullet}\) = 200m/s, \(M_{block}\) = 0.95kg and \(V_{block}\) = 0 for an inelastic collision \(M_{bullet} \times V_{bullet} + M_{block} \times V_{block} = (M_{bullet} + M_{block})\)v 0.05 x 200 + 0.95 x 0 = ( 0.05 + 0.95)v 10 + 0 = v v = 10m/s K.E of the block = \(\frac{1}{2}mv^2\) K . E = \(\frac{1}{2} \times(0.05 + 0.95) \times10^2\) ( bullet now part of the block) K . E = \(\frac{1}{2} \times1 \times100\) = 50J

The Rutherford scattering experiment showed that the nucleus of an atom: is concentrated in a tiny volume and is positively charged. In the experiment, when alpha particles were fired at a thin gold foil, most of the alpha particles passed straight through, but a few were deflected considerably. This result led Rutherford to conclude that the positive charge of the atom is concentrated in a small, dense nucleus at the center of the atom. The fact that some alpha particles were deflected strongly indicated that there was a positively charged nucleus within the atom. This experiment was crucial in developing our understanding of atomic structure and led to the model of the atom with a central nucleus containing protons and neutrons, surrounded by electrons.

The force of attraction between the nucleons (protons and neutrons) in the nucleus of an atom is called the nuclear force or strong nuclear force. This force is responsible for holding the protons and neutrons together in the nucleus despite the electrostatic repulsion between positively charged protons. It is one of the fundamental forces in nature and plays a crucial role in the stability of atomic nuclei.

When an electron jumps directly from an orbit of n = 4 to n = 2, a photon is emitted. This is a typical scenario in atomic physics where an electron transitions from a higher energy level (orbit) to a lower energy level. During this transition, the electron loses energy, and this energy is emitted in the form of a photon. The energy of the emitted photon corresponds to the energy difference between the two energy levels, as described by the quantization of energy levels in the Bohr model of the atom.

Acceleration of A = a Acceleration of B = 2a (given) then: \( S_A = 0 \times t + \frac{1}{2}at^2 = \frac{1}{2}at^2\) \( S_B = 0 \times t + \frac{1}{2} \times2at^2 = at^2\) \(t^2 = t^2 ⇒ \frac{2S_A}{a} = \frac{S_B}{a}\) ⇒ \(2S_A = S_B\) ( as a cancels out)

The part of the human eye that performs a function similar to the diaphragm in a camera lens is the Iris. Just like the diaphragm in a camera lens controls the amount of light entering the camera, the iris in the eye controls the amount of light that enters the eye by adjusting the size of the pupil. It can contract or expand to regulate the size of the pupil in response to varying light conditions, thus controlling the amount of light that reaches the retina at the back of the eye.

The equation f = \(\frac{1}{D}\) is not a correct mirror formula

The device associated with alternating currents (AC) only from the provided options is the step-up transformer. Step-up transformers are specifically designed to work with alternating currents and are used to increase voltage levels in AC systems.

The conclusive test for magnetism in a steel bar suspended horizontally at its midpoint is when the bar always settles in the magnetic N-S (North-South) direction.

The purpose of commutators in a direct current (DC) motor is to reverse the direction of the current after every half rotation.

F = \(kv^xρ^yA^z\) For the left-hand side: F = mass \times acceleration = \(MLT^{-2}\) For the right-hand side: v = \(LT^{-1}\), ρ = \(ML^{-3}\) and A = \(L^2\) So, \(MLT^{-2} = k(LT^{-1})^x(ML^{-3})^y(L^2)^z\) Since k is dimensionless, \(MLT^{-2} = (LT^{-1})^x(ML^{-3})^y(L^2)^z\) \(MLT^{-2} = L^x \times T^{(-1)x} \times M^y \times L^{(-3)y} \times L^{(2)z}\) \(MLT^{-2} = L^x \times T^{-x} \times M^y \times L^{-3y} \times L^{2z}\) \(MLT^{-2} = L^{(x - 3y + 2z)} \times T^{-x} \times M^y\) \(M^1L^1T^{-2}= L^{(x - 3y + 2z)} \times T^{-x} \times M^{y}\) Comparing the powers: For M, y = 1 For L, x - 3y + 2z = 1 ---- (i) For T, -x = -2 ∴ x = 2 Substitute (2) for x and (1) for y in equation (i) ⇒ 2 - 3(1) + 2z = 1 ⇒ 2 - 3 + 2z = 1 ⇒ -1 + 2z = 1 ⇒ 2z = 1 + 1 ⇒ 2z = 2 ∴ z = 1 Hence, x = 2, y = 1 and z = 1.

a. Strain energy is the potential energy stored within an elastic material as a result of its deformation caused by external forces. b. Energy stored E = \(\frac{1}{2}Fe\) Young Modulus = \(\frac{ Stress}{ Strain}\) = Y Stress = \(\frac{Force}{Area} = \frac{(F)}{(A)}\) Strain = \(\frac{ Extension}{Original Length} = \frac{(e)}{(l)}\) Y = \(\frac{F}{A}\div \frac{e}{l}\) Y = \(\frac{F}{A} \times \frac{l}{e}\) F = \(\frac{YAe}{l}\) Therefore, Energy stored E = \(\frac{1}{2}\frac{YAe}{l}\times e\) E = \(\frac{YAe^2}{2l}\)

i. From v = u + gt: \(u_x\) = ucos\theta, g = 0 (horizontal component is not affected by gravity) \(v_x\) = ucos\theta + (0)t ∴ \(v_x\) = ucos\theta ii. \(v_y = u_y + gt\) ∴ \(v_y = usin\theta + gt\) b. It assumes that the only force acting on the projectile is gravity, and there are no other forces, such as air resistance or drag, affecting its motion.

Geostationary satellites Polar satellites 1 They orbit the earth directly above the equator in geosynchronous orbit. they remain fixed relative to a specific point on the Earth's surface They orbit the Earth, passing over or near the north and south poles on each orbit. 2 They have an inclination of 0^\circ, meaning their orbital plane aligns with the equatorial plane They have a high inclination angle( usually around 90^\circ) to achieve polar orbits. 3 They observe the Earth from a fixed position, providing a continuous view of a specific region. They observe the Earth from a changing perspective as the orbit, resulting in different views of the Earth's surface with each pass 4 They primarily collect data for meteorological observation weather forecasting, and telecommunications. They collect data for a wide range of applications, including weather monitoring, climate research, Environmental monitoring, and scientific research. 5 They are positioned at an altitude of approximately 35,786 kilometres above the Earth's surface. They operate at a lower altitudes, typically between 700 and 1500 kilometers 6 They provide a continuous stream of data and observations for a specific region, allowing for real-time monitoring. They have a lower data refresh rate since they pass over a given less frequently. However, they provide a broader coverage. pick any three according to the given instructions.

a. According to the kinetic theory, diffusion in fluids occurs because of the random and continuous motion of molecules. This motion results in a net movement of the molecules from regions of higher concentration to regions to regions of lower concentration ultimately leading to the mixing of substances in the fluid i.e. the process continues until the concentration becomes uniform throughout the fluid. It's driven by the kinetic energy of the molecules and leads to the mixing of substances in fluids. b. i. Interference of light waves ii .– Photo-electric effect –Compton Effect