**Understanding Gravity**

- When a boy accidentally drops a book from his hand. The book is pulled towards the Earth by the
**force of gravity**.

**Fig.**The book dropped by the boy is pulled towards the Earth - The force of gravity on the Earth is caused by a gravitational field around the Earth. The
**gravitational field**is a region in which an object experiences a force due to the gravitational attraction towards the centre of the Earth. Figure shows the direction of the gravitational field.**Fig.**The direction of the gravitational field around the Earth **Gravitational acceleration**is the acceleration of an object due to the pull of gravitational force.- An object undergoes
**free fall**if it is acted upon by gravitational force only. Near the surface of the Earth, all free falling objects will have a gravitational acceleration, g which is equal to 9.8 m s^{-2}. - Figure shows a stroboscopic photograph of a feather and an apple undergoing free fall in a vacuum. Both the feather and the apple fall with the same acceleration.

(A stroboscopic photograph captures the image of a moving object and shows its respective positions at regular intervals of time.)

- The
**gravitational field strength**at a point in the gravitational field is the gravitational force acting on a mass of 1 kg placed at that point. Therefore,

Where, g = gravitational field strength,

F = force of gravity, m = mass. - The SI unit for gravitational field strength is N kg
^{-1}.

**Also Read About:** Newton’s Law of Universal Gravitation

Earth’s Gravitational Force

**Weight**

- The weight of an object is the force of gravity acting on the object.
- For an object with a mass, m, its weight, w is given by:

**w = mg**

where g is the gravitational field strength. - The SI unit for weight is newton (N). Weight is a vector quantity.

**Example 1.** An astronaut has a mass of 75 kg. Calculate the gravitational force on the astronaut when he is standing

(a) on the Earth with a gravitational field strength of 9.8 N kg^{-1},

(b) on the Moon with a gravitational field strength of 1.6 N kg^{-1}.

**Solution:**

**Example 2.** The Hubble telescope has a mass of 11600 kg.

(a) Determine its weight when it is resting on Earth which has a gravitational field strength of 9.8 N kg^{-1}.

(b) What is the value of the gravitational field strength if its weight at a particular orbit above the Earth is 95000 N?

**Solution:**

**Example 3. **At a particular point above the Earth, an aircraft of mass 20 000 kg experiences a gravitational force of 192 000 N. Calculate the gravitational field strength at that point.

Solution:

**Example 4.** A ball is dropped from a building and undergoes free fall. What is its velocity just before it touches the ground which is 100 m from where it is dropped?

[g = 9.8 m s^{-2}]

**Solution:**

**Activity 1**

**Aim:** To determine the value of acceleration due to gravity.

**Materials:** Slotted masses, a piece of plank, cellophane tape, ticker tape

**Apparatus:** Ticker timer, 12 V a.c. power supply, stool, G-clamp

**Method:**

- The apparatus is set up as shown in Figure.
- A strip of ticker tape about 2.5 m long is cut and passed through the ticker timer.
- One end of the tape is attached to the 100 g slotted mass.
- The ticker timer is switched on and the slotted mass is released so that it falls onto the plank.
- The tape is analysed to determine the gravitational acceleration, g.
- Steps 2 to 5 are repeated for slotted masses of mass, m = 200 g and 300 g.

**Results:**

**Discussion:**

- The values of g for different masses are almost the same. This shows that the gravitational acceleration is constant. It does not depend on the value of the mass.
- The accurate value for g is 9.8 m s-2. The experimental values are smaller than this value due to unavoidable frictional forces and air resistance.