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].

(a) (i) Define Optical angle.

(ii) Explain two conditions necessary for total internal reflection to occur. 

(iii) List three practical applications of total internal reflection.

(b) State two effects of refraction. 

(c)(i) Define progressive waves.

(ii) A plane progressive wave is represented by the equation y = 0.5 sin(1000\(\pi\)r = \(\frac{100 \pi \lambda}{17}\)) where y is in millimetres, t in seconds and x in metres.  Calculate the: (\(\alpha\)) frequency of the wave; (\(\beta\))of the wave; (\(\gamma\)) speed of the wave

(a) In an experiment to measure the specific latent heat of vapourisation of water, a student places a heater in a beaker containing water.  The beaker stands on an electronic balance so that the mass of the beaker and water could be measured. The heater is switched on and readings were taken every 100s when the water starts boiling.

The table below shows the readings.

(I) Fill in the mass of water evaporated.

(ii) Given that the heater supplies energy at the rate of 38J/s, fill in the values of the energy supplied by the heater in 100s, 200s, 300s, and 400s. 

(ii) Plot a graph of energy supplied on the vertical axis and mass of water evaporated on the horizontal axis, starting both axes from the origin(0,0). 

(iv) Determine the slope of the graph.

(v) what does the value of the slope mean?