V-R Puting eq. (4) and (6) in (5), we get g/G xR 4/3 Tt R 3g 47t RG (7) Calculations: 3x 9.8 Average density of earth, p = 4x 3.14 x 6.37 x 10° x 6.67x 10 e=5.52 x 10 kg MASS OF THE SUN: Using the law of gravitation, determine mass of the sun. Suppose Ms is the mass of the sun. Let R be the Earth distance between centers of the earth and the sun orbital radius of the earth. As the earth is

revolving round the sun, then gravitational force = centripetal force FE Fe

..(1) Sun Now, the force of gravitaticnal attractionis G MM The centripetal acceleration of the earth (27TR/T) Velocity= Circumference 27 time period Where T is the time of one revolution of the eartharound the su = 365.3 days and R = 1.5 x 10"m) Me a FMTFe=--- (3) Comparing(2) and eq (3Suppose the earth is a sphere homogeneous composition. At the earth's surface, acceleration due to gravity, GMe Earth where Me is mass of the earth, Re is radius of the earth, and M Gis the universal gravitational constant. At a height 'h' above the earth's surface, the changed value of 'g' is where R = R +h... Dividing eq.  by (1), we have GMe/R (Re, we have9required to hold an object from the restraining force which gives the impression of welg WEIGHTLESSNESS IN AN ELEVATOR An elevator is a non-inertial frame of reference moving up or down with some acceleration. tne ceiling of an elevator. The reading of the spring balance will give the tension that is acting upward on the block. Consider a block of mass 'm' suspended from a spring balance that is attached to CASE I: WHEN ELEVA TOR IS AT REST Suppose the elevaror is stationary (a = 0). Consider the forces acting on the suspended block. (1) Weight (W), acting vertically downward. (il) Tension (T). acting upward along the spring The tension is equal but opposite to thc force of gravity (W). This represents the "truc weight" of the bleck

Since net force in zero, hence T-mgConclusion: The 'apparent weight' and true weight are identical