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(a) its geometric centre 

(a) At its geometrical centre

Speed

Hint: Speed is scalar but velocity and acceleration are vector quantities. So, speed remains constant but velocity and acceleration change with the change in direction, and in circular motion the direction of motion changes at every point.

Work is said to be done only when the force applied on a body makes the body move. It is a scalar quantity.

(a) On standing outside the disc, we find that the pebble is moving on a circular path. On standing at the centre of the disc, we find that the pebble is stationary placed just in front of us.

No, centrifugal force is a fictitious force.

(d) The assertion is false, but the reason is true

(b) Treads on a tyre

Friction can be classified into two basic types: 

1. Static friction 

2. Kinetic friction. 

1. Static friction : The friction experienced by the bodies, which are at rest is called static friction. (E.g : All the objects rigidly placed to be at rest on the Earth, a knot in a thread. 

2. Kinetic friction : Friction existing during the motion of bodies is called kinetic friction. 

Further, kinetic friction can be classified into two:

• Sliding friction 
• Rolling friction.

1. Sliding friction : When a body slides over the surface of another body, the friction acting between the surfaces in contact is called sliding friction. 

2. Rolling friction : When a body rolls over another surface, the friction acting between the surfaces in contact is called rolling friction. Rolling friction is less than sliding friction. That is why wheels are provided in vehicles, trolleys, suitcases etc.

The rolling friction is smaller than sliding friction, sliding is replaced by rolling with the usage of ball bearings. So lead shots are used in the bearing of a cycle hub.

Friction is a necessity in most of our day to day activities. It is desirable in most situations of our daily life. 

1. We can hold any object in our hand due to friction. 

2. We can walk on the road because of friction. The footwear and the ground help us to walk without slipping. 

3. Writing easily with a pen on paper is due to friction.

4. Automobiles can move safely due to friction between the tyres and the road. Brakes can be applied due to frictional resistance on brake shoes. 

5. We are able to light a matchstick, sew clothes, tie a knot or fix a nail in the wall because of friction.

Though it is giving a negative effect, in most of our day to day life friction helps us to make our life easy. So, it is called as “necessary evil”.

Disadvantages of friction: 

1. Friction wears out the surfaces rubbing with each other, like screws and gears in machines or soles of shoes. 

2. To overcome the friction an excess amount of effort has to be given to operate a machine. This leads to wastage of energy.

 A large force is required to stop the loaded vehicle. It is because loaded vehicle has greater momentum than the empty vehicle as the mass of loaded vehicle is more than that of the empty one. So, it requires more force to stop.

Luggage on the top of the bus is not a compact part of the bus. When a moving bus takes a sharp turn or suddenly applies brakes to stop, the luggage placed loosely on the roof of the bus continues moving forward (inertia of motion) and is likely to fall off the bus. Conversely, if a stationary bus accelerates suddenly, the luggage tends to remain in the same state (inertia of rest) and hence slides backward To avoid falling of luggage off the bus, it is advised to tie it with a rope.

The water will not overflow when the ice melts. The water level will remain the same. Ice floats on water because its density is less than that of water. When ice melts, the volume of the water formed is less than the volume of the ice which has melted.

When ice in water melts, this difference equals the volume of the water formed when the part of ice above the surface of water melts. Therefore, the water level remains the same. Hence, there is no overflow of water when the ice melts.

The pressure produced by a given force depends on the areas of the surface on which the force acts. The less the surface area, the greater is the pressure produced. A needle has a sharp point so that the area is decreased and hence the pressure is increased. This makes the action of piercing easier.

1. It is easy to cut vegetables. fruits with a sharp knife. A blunt knife does not work here. 

2. The force exerted perpendicularly on a unit area is called ‘pressure’

Pressure = \(\cfrac{Force}{Area\,on\,which\,the\,force\,in\,applied}\)

3. Presently we are considering only the force acting on an area in a direction perpendicular to it.

a. Because of the friction between ground and feet

b. When the area decreases pressure increases. As the area of the edge of the knife is veiy less, it is easy to cut

c. When the area of surface increases pressure decreases, so when more wheels are used it won’t depressed in soil.

d. Because of the friction between the area of contacts.

It is easier to cut with a sharp knife than with a blunt one because, for the same applied force, the pressure exerted (force/area) is more in the case of the sharp knife than in the case of a blunt one.

The effect of a given force varies l inversely as the area of the surface on ( which the force is applied. The less the surface area, the greater is the effect of the force. The cutting edge of a sharp ’ knife has less cross sectional area relative to that of a blunt knife. Hence, it is easy to cut vegetables, fruits with a sharp knife, rather than with a blunt knife. For a given force, pressure is inversely proportional to the area of the surface on which the force acts.

A sharp axe has a sharp edge which means edge has a minimum area as compared to the rest of the axe. As the area is small, the pressure is large and thus easier to cut trees. Whereas blunt axe has larger edge thus exerting less pressure and hence it takes time to cut trees.

A sharp tip is provided at the end of a pin so that pressure (FORCE / AREA) exerted by it is maximum when it is pressed by a given force.

The buoyant force depends upon the volume of the object immersed in the fluid (V), the density of the fluid (ρ1) and the acceleration due to gravity (g) at that place. 

[Note: Magnitude of the buoyant force = Vρ1 g.]

When a body is suspended in air, the buoyant force acts on the body. Hence, the magnitude of the net downward force on 1 the body = the magnitude of the weight of the body – the magnitude of the buoyant force on the body. Hence, when a spring balance is used to weigh a body, the weight of the body in air is less than that in vacuum.

Proceed as above. 

ρ (body) = \(\cfrac{200\,g}{400\,cm^3}\) = 0.5 g/cm³

It is less than the density of water. 

∴ The body will float in water.

Data: m = 200 g, V= 50 cm³.

ρ (water) = 1 g/cm³

Density(ρ) = \(\cfrac{mass}{volumee}\)

∴ ρ (body) = \(\cfrac{200}{50\,cm^3}\)

It is greater than the density of water. 

Hence, the body will sink in water.

It sinks in the water.

False It is not easier to hammer a blunt nail into a piece of wood than a sharply pointed nail.

1. When a bucket full of water is immersed in water, the net force acting on the bucket = weight of the bucket full of water-the buoyant force exerted by the water on the bucket. The buoyant force due to a fluid is proportional to the density of the fluid.

2. The density of water is much greater than that of air. Therefore, the buoyant force acting on a bucket full of water while it is in water is much greater than that when it is out of water, i.e., in air. Hence, it appears to weigh less, while it is in water than when it has been pulled out of water.

Working of the lactometer and hydrometer is based on Archimedes’ principle.

Archimedes’ principle: When an object is partially or fully immersed in a fluid, a force of buoyancy acts on it in the upward direction. This force is equal to the weight of the fluid displaced by the object. 

[Note: The two forces mentioned here are equal in magnitude and opposite in direction.]

1. The working of a lactometer, a device used to determine the purity of a sample of milk, and a hydrometer, a device used to determine the density of a liquid, is based on Archimedes’ principle. The extent to which a lactometer floats (or sinks) depends on the density (and hence purity) of the milk. The same thing is true for a hydrometer. The greater the density of a liquid, the less is the extent to which a body sinks in it.

2. Archimedes’ principle is used in design of ships and submarines. A submarine is provided with large tanks at the front and the back. Its weight can be increased by filling the tanks with sea water or air from compressed air reservoirs. The weight can be decreased by pumping out water from the tanks by forcing compressed air in them. By controlling the weight, it can be made to sink or rise to the surface as desired.

3. The density of a body that floats or sinks in water or kerosine can be determined by. Archimedes’ principle. 

4. The density of kerosine can be determined by Archimedes’ principle, using a body of material that is not affected by water and kerosine.

Archimedes’ principle is used in the construction of ships and submarines. The working of the lactometer and hydrometer is based on Archimedes’ principle.

[Note: The hydrometer is used to determine the density or relative density of a liquid.]

The eraser gets smaller and smaller as we use it more and more due to frictional force causing wear and tear of the eraser.

When a force is applied on a stationary body, it begins to move.

Ways to reduce friction: 

1. Providing ball bearings or wheels between the moving parts of machine or vehicles reduce friction and allow smooth movement as rolling friction is less than sliding friction. 

2. Oiling or lubricating (with graphite or grease) the moving parts of a machine reduces friction. Fine powder like talcum powder also works as a lubricant to reduce friction. 

3. Polishing the rough surface reduces friction offered by it. 

4. Streamlining (giving special shape to experience minimum drag) the bodies of aeroplanes, cars, boats and ships help reduce drag (fluid friction) while travelling through air or water.

(a) Muscular force

(b) Frictional force

(c) Gravitational force.

(d) Electrostatic force

(e) Force of tension.

(f) Muscular force

(g) Magnetic force

(h) Muscular force

(i) Gravitational force

(j) Muscular force.

When a force is applied on a moving body, it can be made to stop or it can change the direction of motion.

Disadvantages of friction:

1. Friction produces heat which damages the moving parts of a machine. 

2. Friction produces wear and tear on the contacting surfaces. This reduces the life of machine parts, tyres and shoe soles. 

3. A lot of energy is wasted due to friction to overcome it before moving.

Friction is of three kinds : 

1. Static friction 

2. Sliding friction, 

3. Rolling friction

When a force is applied on a body which is not free to move, it gets deformed i. e., the shape or size of the body changes.

Two kinds of forces in nature are : 

1. Contact forces 

2. Non contact forces

1. A car originally at rest when pushed, begins to move. 

2. A moving bicycle is stopped by applying the brakes. 

3. The speed of a moving vehicle is slowed down by applying the brakes. 

4. A player kicks a moving football to change its direction of motion. 

5. On stretching a rubber string, its length increases.

(a) The shape and size of catapult changes i.e., its length increases. 

(b) The heavy cart begins to move. 

(c) The direction of the ball changes. 

(d) The speed of the moving cycle is slowed down. 

(e) There is change in size and shape of spring.

Given, AB = 4 m hence, OA = 2m and OB = 2m

Moment of force F (=10N) at A about the point O

= F × OA = 10 × 2 = 20 Nm (clockwise)

Moment of force F (=10N) at point B about the point O

= F × OB= 10 × 2 = 20 Nm (clockwise)

Total moment of forces about the mid-point O=

= 20 + 20 = 40 Nm(clockwise)

Given AO = 2m and OB = 4m

(i) Moment of force F₁(= 5N) at A about the point O

= F₁ × OA

= 5 × 2 = 10Nm (anticlockwise)

(ii) Moment of force F₂ (= 3N) at B about the point O

= F₂ × OB

= 3 × 4 =12 Nm(clockwise)

(iii) Total moment of forces about the mid-point O =

= 12 – 10 = 2 Nm (clockwise)

(i) False. (Pressure due to a given force is inversely proportional to the area on which the force acts.)

(ii) True.

(iii) True.

(iv) True.

(v) True.

The specific gravity of a substance is another name used for relative density, i. e., the ratio of the density of the substance to the density of water.

Force. (Force is a vector quantity; other quantities are scalar quantities.)

The pressure exerted by a liquid at a point inside the liquid depends on the density of the liquid.

F₁ = F₂ = F = 5N force being equal opposite and parallel couple arm = 1.2m

∴ The moment of couple = F x ⊥ distance

= 5 x 1.2

= 6Nm