In this post we are going to show the detailed solution for class 9th science chapter 10. All the solution are prepared by our esteemed who are very well experienced in the teaching.

Summary of the chapter

Gravitation 

Universal Law of Gravitation 

The universal law of Gravitation states that any two bodies having mass attract each other with force directly proportional to the product of their mass and inversely proportional to the square of distance between them. The force acts along the line joining the centers of the objects.

⇒ F ∝  m1 m2 / d²

⇒ F = Gm1m2 / d²

Here, G is Universal gravitational constant = 6.67 × 10^–¹¹ Nm²kg^–². The value of G was found out by Henry Cavendish.

Note:

• If mass of the object is large, force will be more. If mass of the object is small, force will be less.
• If distance between two object is more, force exerted will be less and vice versa.

Importance of Gravitational Force:

• It binds us to Earth.
• Moon revolves around Earth due to gravitational force. Planets revolve around Sun due to gravitational force.
• Tides in seas are caused due to gravitational force of moon on earth.

Free Fall 

The earth attracts object towards it is due to gravitational force. When an object moves such that only gravitational force of earth acts on it, it is said to do “Free Fall”.

Attraction of Earth on Object close to its Surfaces 

When an object is near the surface of earth, the distance between object and center of the earth will be equal to the radius of the earth (i.e.) because the distance of object is negligible in comparison of the radius of the earth.

Therefore,

⇒ F = GM_Em / R_E²

⇒ F = m (GM_E / R_E²)

⇒ F = mg … (i)

Where,

g = acceleration due to gravity.

Value of g = 9.8 m/s²

Velocity and Acceleration

• When an object is moves with constant velocity, such motion is called uniform motion. 
• When an object moves with increasing velocity, motion is called accelerated motion. 
• When an object moves with decreasing velocity, motion is called retarded motion / De-acceleration motion. 

Direction of velocity is the direction in which body is moving.

Falling Bodies

Case 1: When an object is released from top, it falls down due to gravitational force of earth. As force acts downwards, acceleration ‘a’ would be in downward direction.

As object is moving downward and acceleration is also in downward direction, velocity increases. So when an object is released from top, it does accelerated motion (increasing velocity). 

Calculation of acceleration ‘a’: 

According to Newton’s 2nd Law

⇒ F = ma

⇒ a = F/m

From equation (i)

⇒ a = mg/m

⇒ a = g = 9.8 m/s²

Thus, acceleration acted on a falling object is equal to ‘g’ (acceleration due to gravity).

Case 2: If we throw a ball upward in the air, a gravitational force acts downward on it. As force acts downwards, acceleration is in downwards direction. It means velocity will decrease with with and at one point, it becomes zero.

Due to the gravitational force, the ball takes U-turn and reaches to ground with same speed with which it was thrown up. As object is moving downward and acceleration is also in downward direction, velocity increases.

Note:  We have studied three equations of motion.

⇒ v = u + at 

⇒ s = ut + ½ at² 

⇒ v² = u² + 2 as 

These equations can be used to calculate the value of velocity, distance and time, etc. by replacing “a” by “g” and “s” by “h”

⇒ v = u + g × t 

⇒ h = u × t + ½ gt²

⇒ v² = u² + 2 g × h 

The value of ‘g’ is taken as positive in the case of object moving towards earth and taken as negative in the case of object is thrown in opposite direction of earth.

Air Resistance 

Theoretically, all object of different shape, size and mass should take same time to fall through same distance. But practically it is observed that two object of different mass hit the ground at different times due to air resistance on them.

Factors affecting Air resistance: 

1. More the mass, lesser the effect of air resistance.
2. More the surface area of object, more the effect of air resistance.

Variation in the value of ‘g’

• As we go at large heights, g decreases.
• Since, earth is not a perfect sphere rather it has oblique shape. Therefore, radius at the equator is greater than at the poles. Since, value of ‘g’ is reciprocal of the square of radius of earth. Thus, the value of ‘g’ will be greater at the poles and less at the equator.
• Geography of earth is different at different locations such as mountains, plains, oceans. This causes variation in value of g.

Mass and Weight 

Mass

Mass is the quantity of matter present. The mass of a body is always constant and does not change from place to place. Mass has no direction and thus it is scalar quantity. The SI unit of mass is kg. Mass can be measured using beam balanced.

Weight

Weight of an object is the gravitational force applied by the earth on that object.

W = m × g

The weight of a body changes from place to place, depending on mass of object.

Since weight always acts vertically downwards. Therefore, weight has both magnitude and direction and thus, it is a vector quantity. The SI unit of weight is Newton. Weight can be measured using spring balance.

Weight of an object on the surface of the Moon 

Mass of an object is same on earth as well as moon, but weight is different.

Weight of body on Earth / Weight of body on Moon = ( GM_Em/R_E² ) / ( GM_Mm/R_E² ) =  M_ER_M² / R_E²M_M 

⇒ (6 × 10²⁴kg) / (6.37 × 10⁶ m)²  (1.74 × 10⁶m)² / (7.36 × 10²²kg )

⇒ (6 × 10²⁴kg) / ( 6.37 x 10⁶m )²  (1.74 x 10⁶m )² / ( 7.36 x 10²²kg )

⇒ Weight of body on Earth / Weight of body on moon = 6

⇒ Weight of body on Earth = 6 (Weight of body on moon)

Or, Weight of body on moon = 1/6 (Weight of body on Earth)

Circular Motion and Gravitational Force

In circular motion, a force must act on body as its direction of velocity changes. This force is called Centripetal force.

When moon revolves around earth in circular path, gravitational force of earth provides the centripetal force to moon for circular motion.

When planets revolves around sun, gravitational force of sun provides the centripetal force to planets.

Thrust and Pressure

Thrust: Force exerted by an object perpendicular to the surface is called thrust.

Pressure: Pressure is defined as thrust or force per unit area on a surface.

Pressure = Thrust / Area

SI unit of pressure = Nm² = Nm^-2 = Pascal (Pa)

Since, pressure is indirectly proportional to the surface area of the object. So, pressure increases with decreases in surface area and decreases with increase in surface area.

Pressure in Fluids:

Anything that can flow is called Fluid like liquid and gases.

Molecules of fluid move around and collide with walls of vessel. Thus, fluids apply pressure on walls. Fluids exert pressure in all directions.

Buoyancy and Buoyant Force: Fluids applies an upward force on a solid which is partially of fully submerged in liquid. This phenomenon  is called buoyancy (up-thrust) and applied upward force is called buoyant force.

Experiment – 1:   

Take a empty bottle and float it on water. If we push it down in the water partially or fully and then release, bottle suddenly jumps upward. This is because the water applies an upward force on bottle.

Experiment – 2: 

Hang a rubber string. Attach a stone to the rubber string. String will elongate. Submerge the stone in water – filled bucket. The elongation in string decreases.

This happens due to upward buoyant force of water.

Archimedes Principle 

When an object is fully or partially submerged in a liquid, buoyant force acts on it in upward direction. Its value is equal to weight of liquid displaced.

For example, suppose an object is partially submerged in a liquid and the mass of displaced liquid is 1.5 kg. Then buoyant force applied on the object (F) = Weight of liquid displaced = m × g

⇒ (1.5) × (9.8) = 14.7 N

Archimedes principle has many uses. It is used in designing ships, submarines, air balloons, etc.

Density 

The density of a substance is the mass of a unit volume of the substance.

Density = Mass / Volume

Every material has its own density. The SI unit of density is kilogram per meter cube (kg m ^-3).

Relative Density 

The relative density of a substance is the ratio of the density of a substance to the density of water.

Relative Density = Density of a substance / Density of water

Since relative density is a ratio of similar quantities, it has no unit.

You can see other posts here:

• NCERT Class 9th Science Chapter 8 – Motion Summary
• NCERT Science Class 9th Chapter 8 Motion
• NCERT Science Class 9th Chapter 9 Force and Laws of Motion Summary
• NCERT Science Class 9th Chapter 9 Force and Laws of Motion

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