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Define intensity of gravitation and write its equation, unit and dimensional formula |
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Answer» Solution :`implies` The force is exerted MUTUALLY on two bodies separated by some distance is explained to occur through the field as under: (1) Every object produces a gravitational field around it, due to its mass. (2) This field exerts a force on ANOTHER body lying in this field. `implies` Intensity of gravitational field : .The gravitational force exerted by the given body on a body of unit mass at a given point is called the intensity of gravitational field `(VECI)` at that point.. It is also known as gravitational field or gravitational intensity. `implies` Suppose a body of mass M at the origin of coordinate system 0 and a body of mass m= 1 kg is placed at point P having position vector `vecr`  `implies` Gravitation force on bodies of mass m and M, `vecF=(GMm)/(r^2)hatr` If `m = 1 kg, vecF = vecI` intensity of gravitation . `:. vecI=-(GM(I))/r^2hatr""...(1)` `implies` Here, force of body of mass M on the body of mass m is toward O, whereas position vector and unit vector is from 0 to P and HENCE native sign is present in formula. `implies` And the value of intensity of gravitation `I= (GM)/r^2 ""...(2)` `implies` Its unit : `N/(kg)` fe and dimensional formula `M^(0) L^(1) T^(-2)`. If a body of mass m is put at this point `P_1`the gravitational force exerted by the field on it is `vecF = vec(Im) =- (GMm)/r^2hatr` `implies`Equation (2) shows that the gravitational intensity due to earth at a point has the same value as the gravitational ACCELERATION (g) at that point. `implies` Here, gravitational intensity and gravitational acceleration are different quantities but their units and dimensional formula are equivalent. `implies` For both `I rarr rand grarr r `graph are same. |
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