A satellite launched with velocity V\(_E\) just escapes the earth's gravitational attraction. Given that the radius of the earth is R, show that V\(_E\) = \(\sqrt{20R}\) [g = 10ms\(^{-2}\)

A bullet is fired from a gun at 30\(^o\) to the horizontal. The bullet remains in flight for 25s before touching the ground. Calculating the velocity of projection. [g = 10ms\(^{-2}\)]

State three properties of lasers that make them preferable to ordinary light beam.
 

(a)i) Define a torque.

(ii)State three factors that determine a torque

(b)(i) Define free fall.

(ii) A body is thrown vertically upwards from the top of a tower 40.0m high with a velocity of 10.0ms\(^{-1}\). Calculate the time taken for the body to reach the ground. [g.= 10.0ms\(^{-2}\)]

c) A cube of wood of side 8.0cm, floats at the interface between oil and water with 2.0cm of its surface below the interface as shown in the diagram below. Given that the relative densities of oil and water are 0.72 and 1.00 respectively, calculate the mass of the wood

(a)Explain resonance frequency as applied in RLC series Circuit. 

(ii) Sketch a diagram to illustrate the variation of frequency, f, with the resistance, R, the capacitive reactance, X\(_c\) and the inductive reactance X\(_L\), in RLC series circuit.

(iii) Using the diagram drawn in (a)(ii) state whether the current in the circuit leads, lags or is in phase with the supply voltage when: (\(\alpha\)) f = f\(_o\); (\(\beta\)) f < f\(_o\) ; (\(\gamma\))f\(_o\); when f\(_o\) is the resonant frequency.

b)(i) Define mutual inductance.

(i) The coil of an electric generator has 500 turns and 8.0cm diameter. If it rotates in a magnetic field of density 0.25T, calculate the angular speed when its peak voltage is 480V. [\(\pi\) = 3.142].