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Weight of a body on the Earth is given by:

W = mg

Where,

m = Mass of the body

g = Acceleration due to gravity

The value of g is greater at poles than at the equator. Therefore, gold at the equator weighs less than at the poles. Hence, Amit’s friend will not agree with the weight of the gold bought.

• If a body has to move in a curved path, its direction of velocity must change continuously. 
• This is done by the centripetal force. 
• Hence an object cannot move along a curved path if no force acts on it.

When the centre of gravity of the ladder and the centre of gravity of our body lies in the same line then we can balance the ladder on our shoulders.

• Take a ladder. 
• Find the mid stick by counting the sticks of the ladder. 
• Put that mid stick on the shoulder and balance the ladder. 
• That is the center of gravity of a ladder.

According to Newton’s third law of motion, “Every object exerts equal and opposite force on other object but in opposite direction.

” According to Newton’s law of gravitation, “Every mass in the universe attracts the every other mass.” 

In case of freely falling stone and earth, stone is attracted towards earth means earth attracts the stone but according to Newton’s third law of motion, the stone should also attract the earth and really it is true that stone also attracts the earth with the same force F = m × a but due to very less mass of the stone, the acceleration (a) in its velocity is 9.8 m/s² and acceleration (a) of earth towards stone is 1.65 × 10^-24 m/s² which is negligible and we cannot feel it.

(d) Both A and B are wrong.

EXPLANATION: 

(A) is wrong because the value of V at the center is -3GM/2a and it increases continuously to -GM/a at the surface and from -GM/a at the surface to zero at the infinity. So it is continuous.          

(B) is wrong because the value of E increases linearly from zero at the center to GM/a² at the surface, then decreases from GM/a² at the surface to zero at the infinity. So it is also continuous.

Work done, W = 24.2 J 

Distance, s = 20cm = 0.2m 

Force = F 

Work done, W = Fs 

F = W/s = 121N

Mass of boy, m = 40 kg 

Height, h = 1.5m 

Acceleration due to gravity, g = 10 m/s² 

a) At highest point velocity, v = 0 

Therefore, KE = 0 

b) PE = mgh = 600J

a) Potential energy 

b) Both potential and kinetic energy

a) Work is said to be done when applied force results in the motion of the body or change in the shape and size of the body. 

Work done is given as: 

W = mgh 

Where, 

W is the work done 

m is the mass of the body 

g is the acceleration due to gravity 

h is the height 

b) Force, F = 2N 

Distance, s = 10cm = 0.1m 

Work done, W = Fs = 0.2 J

The force acting on a body perpendicular to its surface is called thrust. 

The SI unit of thrust is newton (N).

A mug full of water appears light as long as it is under water because buoyant force acts on it which reduces its effective weight and makes it appear lighter.

a) When the displacement of a body is at right angle to the direction of force acting on it, then the work done will be zero. 

b) Force, F = 50N 

Distance, s = 4m 

Angle between direction of force and direction of motion, θ = 60 degree 

Work done, W = F cos θ s = 100 J

a) Energy is defined as the ability to do work and joule is the SI unit of energy. 

b) Following are the various forms of energy: 

Kinetic energy, potential energy, nuclear energy, electrical energy, chemical energy, sound energy, light energy, and heat energy. 

c) Let the mass of both the bodies be m 

Velocity of body 1, v₁ = v 

Velocity of body 2, v₂ = 2v

KE₁ = 1/2 mv² = 1/2 m(v₁) ² 

KE₂ = 1/2 mv² = 1/2 m(v^₂)² 

Ratio = KE₁ : KE₂ = 1/4

a) Kinetic energy of a body is the energy due to motion. 

b) The kinetic energy of the body will be equal to zero as kinetic energy is directly proportional to the square of the velocity. Therefore, when a body is thrown vertically upwards, the kinetic energy becomes zero. 

c) Speed of horse = speed of dog = v 

Weight of dog = m 

Weight of horse = 10m 

KE₁ is the for dog = 1/2 mv² 

KE₂ is for horse = 1/2 mv² = 1/2 (10m)v² 

Ratio = KE₁ : KE₂ = 10/1

The correct answer is a) acceleration

a) The energy stored in a body due to either its position or change in shape is known as potential energy. Water stored in a reservoir is an example of potential energy. 

PE = mgh 

Where, 

PE is the potential energy 

m is the mass of the body 

g is the acceleration due to gravity 

h is the height above the surface of the earth 

b) Following are the differences between kinetic energy and potential energy: 

i) Kinetic energy is defined as the energy in body due to its motion while potential energy is defined as the energy due to its position. 

ii) Kinetic energy of a body when it is at rest is zero whereas the potential energy of a body when it is at rest is not zero.

c) Mass of ball, m = 0.5 kg 

Speed, v₁ = 5 m/s 

Speed, v₂ = 3 m/s 

KE₁ = 1/2 m(v₁₎² 

KE₂ = 1/2 m(v₂)² 

Change in KE = KE₁ – KE₂ 

= 4J

a) Gravitational potential energy is the potential energy due to the position of the body above the ground. While elastic potential energy is the potential energy due to change in the shape and size of the body. Storing of water in the overhead tank is an example of gravitational potential energy while stretching of a rubber band is an example of elastic potential energy. 

b) Work done, W = 784J 

Mass, m = 20 kg 

g = 9.8 m/s² 

W = mgh 

h = W/mg 

h = 4m

The correct answer is a) does not change

Given, Relative density of gold = 19.3 

Density of water = 10³ kg/m³ 

So, Density of gold = Relative density of gold × Density of water 

 = 19.3 × 10³ 

Hence, density of gold = 19.3 × 10³ kg/m³

The reading on spring balance will be zero. This is because the weight of floating block of wood is fully supported by the liquid in which it is floating and hence it does not exert any force on the spring balance.

The body will sink less in water. This is because the density of water is more than that of kerosene due to which water will exert a greater upward buoyant force on the body.

Archimedes’ Principle 

It states, when a body is immersed fully or partially in a fluid, it experiences a upward force that is equal to the weight of the fluid displaced by it.

Applications of Archimedes’ Principle : 

(i) It is used in determining relative density of substances.

(ii) It is used in designing ships and submarines. 

(iii) Hydrometers and lactometers are made on this principle. 

It is because of this ship made of iron and steel floats in water whereas a small piece of iron sinks in it.

The two equal weights of unequal volumes which are balanced in air, will get imbalanced when they are completely dipped in water because due to their unequal volumes, they will displace unequal volumes of water and hence suffer unequal loss in weight.

(a) Those substances which can flow easily are called fluids. All the liquid and gases are fluids, like water, air etc. 

(b) Archimedes’ Principle : 

When an object is wholly (or partially) immersed in a liquid, it experiences a buoyant force (or upthrust) which is equal to the weight of liquid displaced by the object. Buoyant force on an object = weight of liquid displaced by that object 

(c) If the buoyant force exerted by the liquid is less than the weight of the object, the object will sink in the liquid. If the buoyant force exerted by the liquid is equal to or greater than the weight of the object, the object will float in the liquid.

It is difficult to hold a school bag having a strap made of a thin and strong string because the area and strap is small. Hence large pressure is exerted by the strap on the fingers.

Those substances, which can flow easily, are called fluids. All liquids and gases are fluids. A solid exerts pressure on a surface due to its weight. Similarly, fluids have weight, and they also exert pressure on the base and walls of the container in which they are enclosed. Pressure exerted in any confined mass of fluid is transmitted undiminished in all directions. In other words, a fluid (liquid or gas) exerts pressure in all directions – even upwards.

The upward force exerted by the water on the bottle is known as upthrust or buoyant force.

When a body floats or immerses in a liquid, the pressure on the bottom surface is more than that the pressure on the top surface. Due to the difference in pressure, an upward force acts on the body. This upward force is called upthrust or buoyant force. The buoyant force is equal to the weight of the liquid displaced.

The buoyant force (upthrust) acts through the centre of gravity of the displaced liquid which is known as centre of buoyancy. Due to the upthrust exerted on the body by the liquid, the weight of the body appears to be less when the body is immersed in the liquid.

For example, when we immerse a mug into a bucket of water, the mug filled with water appears to be lighter as long as it is under water. But when it is lifted up out of the water we feel that the mug is heavier. This shows that the weight of the body under water is less than its weight when it is above the surface of water.

LAWS OF FLOATATION

1. The weight of the floating body is equal to the weight of the liquid displaced by it.

2. The centre of gravity of the floating body and the centre of gravity of the liquid displaced (centre of buoyancy) are in the same vertical line.