GSEB Solutions for Class 9 Science and Technology – Force and Laws of Motion

GSEB Solutions for Class 9 Science and Technology – Force and Laws of Motion (English Medium)

GSEB SolutionsMathsScience
Exercise 27:

Solution 1.1:

B. Second
Newton’s second law of motion states that Force = mass x acceleration. Hence we can say that it gives the magnitude of force.

Solution 1.2:

A. kg m/s
Momentum = mass x velocity

Thus, its S.I. unit is kg m/s.

Solution 1.3:

10⁵

Exercise 28:

Solution 1.4:

D. Impulse of force
Impulse of force (I) = Force x Time = Change in momentum

Solution 1.5:

B. 0.5 m/s²

Solution 1.6:

A. Bicycle
Inertia of a body is a property of its mass. Larger the mass of a body more is its inertia. Of the given vehicles, a bicycle has the least mass, and hence the least inertia.

Solution 1.7:

B. 0.4 N

Solution 1.8:

B. Momentum
Both momentum and impulse of force have the same unit, i.e. kg m/s.

Solution 1.9:

C. Law of conservation of momentum
Newton’s second and third law leads to the law of conservation of momentum.

Solution 1.10:

A. Glass surface
Frictional force due to a smooth surface is lesser as compared to that of a rough surface.

Solution 1.11:

A. Mass of the object
Frictional force depends on the material of the two surfaces in contact and the area of contact but not on the mass of the objects in contact.

Solution 1.12:

C. Gum
Gum cannot be used to reduce friction.

Solution 1.13:

A. Mass
Mass is a scalar quantity as it depends only on magnitude.

Solution 2.1:

The resultant force of balanced forces is zero.
Therefore, under the effect of balanced forces, a stationary body remains stationary and a moving body retains its motion with constant velocity.

Solution 2.2:

Newton’s first law of motion defines force as an external effect which can change the state of motion or steady state of a body.

Solution 2.3:

Rate of change of momentum gives the value of resultant force acting on a body.

Solution 2.4:

Impulse of Force = Force x Time
Or,
Impulse of Force = Change in Momentum

Solution 2.5:

The force offered by a surface in contact, which opposes motion is called ‘frictional force’.

Solution 2.6:

When a body rolls over a surface without sliding, the frictional force arising is called the rolling frictional force.

Exercise 29:

Solution 2.7:

Newton’s third law of motion states that during interaction between two bodies, the force exerted by the first body on the second body is equal and opposite to that exerted by the second body on the first body.

Solution 2.8:

The law of conservation of momentum states that in absence of an external force the total momentum of a system, comprising of two or more interacting bodies, is constant.

Solution 2.9:

Unit of force in the SI system is ‘newton’ (N).
Unit of force in the CGS system is ‘g cm/s²‘ or ‘dyne’.

Solution 2.10:

The resultant force acting on the bicycle is zero as the bicycle is moving with a constant velocity.

Solution 2.11:

The direction of motion of a body in motion is in the direction of the resultant external force.

Solution 3.1:

Effects on a body when external forces act on it are:

1. Change in its shape
2. Change in its position
3. Change in its state of motion
4. Change in its velocity

Solution 3.2:

To set a stationary body into motion or to bring a moving body to a halt, contact with the body is necessary. Such forces are called contact forces.
Example: When a batsman hits a ball, there is an increase in the velocity of the ball and the direction of velocity of the ball changes.
When an object experiences force without contact; such a force is called a field force.
Example: When a magnet is kept near some iron-pins, the iron-pins get attracted to the magnet and cling to it.

Solution 3.3:

According to Newton’s first law of motion, an object at rest or in uniform motion will remain at rest or in uniform motion unless an unbalanced force acts on it.
Example: A book kept on a table will remain there until an external unbalanced force acts upon it.
A pendulum keeps moving to and fro in vacuum.

Solution 3.4:

Newton’s second law of motion states that the time of the rate of change of momentum is directly proportional to the resultant external force, and the change in momentum is in the direction of the resultant external force.
Mathematically, it states that the external force acting on a body is equal to the product of mass and acceleration of the body.

Solution 3.5:

Newton’s third law states that for every action, there is always an equal and opposite reaction. The action and reaction act on different bodies.
Examples:

1. When a person walks, he applies force by his feet on the soil (action). At the same time, the soil exerts an equal and opposite force (reaction) on his feet which enables him to walk.
2. A swimmer pushes water backward by his hands (action) and the water in turn exert an equal and opposite forward force (reaction) on the swimmer which enables him to swim.

Solution 3.6:

Law of conservation of momentum states that in the absence of external forces, total momentum of a system comprising of two or more interacting bodies is constant.
Derivation:
Let us consider two moving balls A and B of masses m₁ and m₂ and having initial velocities u₁ and u₂ such that u₂ <u₁.
Suppose the balls collide at some point and there is no external force acting on this system.
Let their final velocities be v₁ and v₂ respectively.
According to Newton’s third law of motion,
Force on ball B due to A = -Force on ball A due to B
Or, F_AB = -F_{BA ……………….}(i)
Total initial momentum before collision(p_i)= m₁u₁ + m₂u₂
Total final momentum after collision(p_f)= m₁v₁ + m₂v₂
According to Newton’s second law,

Thus, we conclude that during the interaction between the two balls, momentum before collision is equal to total momentum after collision. Thus, the momentum of the system is conserved in the absence of external forces.

Solution 3.7:

Advantages of friction:

1. Friction between the tyres and the road enables us to control the motion of vehicles. When brakes are applied, friction helps to stop the vehicles.
2. Friction enables us to write on paper.
3. Friction between the feet and soil enables all animals to walk.

Disadvantages of friction:

1. Motion is opposed.
2. Wear and tear is caused in tyres and footwear due to friction.
3. Friction causes wear and tear in parts of vehicle, machinery etc.

Solution 3.8:

Measures to reduce friction:

1. Grease, oil, graphite etc. are used as lubricants in machines to reduce friction.
2. Ball bearings and roller bearing are used in vehicles and machines to reduce friction.
3. Oil is used to reduce friction in engines.
4. Powder is sprinkled on the board while playing carrom.
5. Vehicles are shaped keeping aerodynamics in mind so that friction with air can be reduced.

Solution 3.9:

• A cricketer pulls his hands back while catching a fast moving cricket ball, because this increases the time of catch i.e., increase in the time taken to bring about a given change in momentum. Hence rate of change of momentum decreases. Thus, a small force is exerted on the hands by the ball.
• A person alighting suddenly from a moving bus falls down due to inertia of motion. This is because the body continues to move forward with the velocity of the bus but the person’s feet are stationary causing imbalance.
• When a skater wears skates, the friction between the feet or rollers of skates and ground is much less. Necessary reaction is not provided by the ground to support the feet. Hence, one cannot walk or run with skates on the feet.

Solution 4.1:

Solution 4.2:

Solution 4.3:

Solution 4.4:

Solution 4.5:

Exercise 30:

Solution 4.6:

Solution 4.7:

Solution 4.8:

Solution 4.9:

Solution 4.10: