(a) Define gravitational field intensity
(b) In an experiment to determine the acceleration of free-fall due to gravity, g, using a simple pendulum of length I, six different values of I were used to obtain six corresponding values of period T. If a graph of I along the vertical axis is plotted against T(^2) on the horizontal axis;
(i) make a sketch to show the nature of the graph,
(ii) write down the equation that relates T, I and g hence obtain an expression for the slope of the graph
(iii) given that the slope of the graph is 0.25, determine the value for g [Take (pi) = 3.142]
(c) A stone, thrown horizontally from the top of a vertical wall with a velocity of 15 ms(^{-1}), hits the horizontal ground at a point 45m from the base of the wall. Calculate the
(i) times of light of the stone
(ii) height of the wall [g = 10ms(^{-2})]
Explanation
(a) The gravitational field intensity at any point on the earth’s field is the gravitational force acting on a unit mass at that point
(b)(i)
(ii) A simple Pendulum of length L, swinging in a vertical plane at a small angle of displacement has a period T given as
(T = 2 pi sqrt{frac{L}{g}})
(T^{2} = frac{4 pi^2L}{g})
L = (frac{gT^2}{4 pi^2})
Slope S of the graph I against (T^2 = frac{g}{4 pi^2})
(iii) g = 4(pi^2)S = 4(3.142)(^2) x 0.25 = 9.87m/s(^{2})
(c)(i) Time t = (frac{distance}{speed} = frac{45}{15}) = 3(s)
(ii) Height h = (frac{1}{2} gt^2 = frac{1}{2} times 10 times 3^3 = 45m)