Question

(d) (i) 1. define the term gravitational field strength. 2. give an expression for the gravitational field strength, g, at a height, h, above the surface of the earth and explain all the symbols used. (ii) an object is dropped from the top of a tall building. explain why 1. the gravitational field strength at the top of the building is the same as on the ground, 2. the acceleration of the object at the top of the building may not be the same as the acceleration near the ground.

Explanation:

1. Gravitational field strength is defined as the gravitational force per unit mass experienced by a small test - mass placed in the field. Mathematically, $g=\frac{F}{m}$, where $F$ is the gravitational force and $m$ is the mass of the test - mass.
2. The expression for gravitational field strength $g$ at a height $h$ above the surface of the Earth is $g=\frac{GM}{(R + h)^2}$, where $G$ is the universal gravitational constant, $M$ is the mass of the Earth, $R$ is the radius of the Earth, and $h$ is the height above the Earth's surface.

(i)1. For a building of typical height (compared to the radius of the Earth, $R\approx6400$ km), the value of $h$ is very small. Since $g=\frac{GM}{(R + h)^2}\approx\frac{GM}{R^2}$ (because $h\ll R$), the gravitational field strength at the top of the building is approximately the same as on the ground.
(i)2. The acceleration of the object at the top of the building may not be the same as near the ground because of air resistance. Air resistance acts in the opposite direction to the motion of the falling object and its magnitude depends on the velocity of the object. As the object falls and its velocity increases, the air - resistance force increases, reducing the net force acting on the object and thus changing its acceleration.

Answer:

1. Gravitational field strength is the gravitational force per unit mass on a small test - mass in the field.
2. $g=\frac{GM}{(R + h)^2}$, where $G$ is the universal gravitational constant, $M$ is the mass of the Earth, $R$ is the radius of the Earth, and $h$ is the height above the Earth's surface.

(i)1. Because the height of the building is small compared to the Earth's radius.
(i)2. Due to the presence of air resistance which affects the net force on the falling object.