 Exams

## Chapter 1 : Force – Answers and Solutions to Exercise 1(A) from Selina for Class 9 Physics ICSE

Question 1 :
What are contact forces? Give two examples.

The forces which act on bodies when they are in physical contact with each other are called contact forces.
For example,
(i) Frictional force
(ii) Force applied by a body on another during collision (Normal Reaction)

Question 2 :
What are non-contact forces? Give two examples.

The forces experienced by bodies even when they are not in physical contact with each other are called non-contact forces.
For example,
(i) Gravitational force
(ii) Electrostatic Force

Question 3 :
Classify the following amongst contact and non-contact forces.
(a) Frictional force
(b) Normal Reaction force
(c) Force of tension in a string
(d) Gravitational force
(e) Electrostatic force
(f) Magnetic force

Contact Forces :
(a) Frictional force
(b) Normal Reaction force
(c) Force of tension in a string

Non-contact Forces :
(d) Gravitational force
(e) Electrostatic force
(f) Magnetic force

Question 4 :
Give one example in each case where
(a) The force is of contact and
(b) Force is at a distance

(a) The force exerted by a body on another during collision is a contact force.
(b) Gravitational force acts between the earth and the sun even though they are lakhs of kilometres apart. Physical contact is not necessary in this case. This is an example of Force at at a distance.

Question 5 :
(a) A ball is hanging by a thread from the ceiling of the roof. Draw a neat labelled diagram showing the forces on the ball and the string.

Question 5 :
(b) A spring is compressed against a rigid wall. Draw a neat and labelled diagram showing the forces acting on the spring.

Question 6 :
State one factor on which the magnitude of a non-contact force depends. How does it depend on the factor stated by you?

The magnitude of a non-contact force depends on the distance of separation between the bodies, It follows the inverse square law with distance, $F \propto \frac{1}{r^{2}}$

Therefore, the magnitude of non-contact force decreases as the separation between the bodies increases.

Question 7 :
The separation between two masses is reduced to half. How is the magnitude of the gravitational force between them effected?

Question 8 :
Define the term “force” ?

Force is that physical cause which changes or tends to change either
(i) the shape or the size or,
(ii) the state of rest or the state of motion of the body.

Question 9 :
State the effects of a force on (i) non-rigid and (ii) rigid body. How does the effect of the force differ in the two cases ?

Every body in the universe is made up of elementary particles with inter-particle space between them. The shape and size of the body depends on this inter-particle spacing.

(i) When a force is applied on a non-rigid body, the inter-particle space changes and hence the dimension of the body changes. In other words, it gets deformed. The force can also produce motion in the body.

(ii) On the other hand, when a force is applied on a rigid body, the inter-particle space does not change between the particles and hence the dimension of the body remains the same. However, the force can cause motion in the body.

Question 10 :
Give one example in each of the following cases:
(a) A force stops a moving body
(b) A force moves a stationary body
(c) A force changes the size of a body
(d) A force changes the shape of a body

(a) A cricketer trying to catch a ball stops it by applying a force with his hands.
(b) Bulls pulling a stationary cart
(c) Force applied by air on balloon to expand it while filling the balloon.
(d) On pressing clay, its shapes changes

Question 11 :
State Newton’s first law of motion. Why is it called the law of inertia?

Newton’s first law of motion states that a body continues to be in its state of rest or of uniform motion in a straight line unless an external unbalanced force is applied on it.

The property by virtue of which a body resists any change in its state of rest or of uniform motion is known as inertia. Newton’s first law states this property because of which it is called the law of inertia.

Question 12 :
Define the term momentum. State its S.I. unit.

The product of mass and velocity of a body at any instant is known as the momentum or linear momentum of the body.

S.I. unit of linear momentum is kg m s-2

Question 13 :
(a) Write an expression for the change in momentum of a body of mass m moving with velocity v if
(i) v << c
(ii) v → c
(b) State the condition when the change in the momentum of a body depends only on the change in the velocity.

(a) As we know the mass of a body is given by the expression : $m = \frac{m_{o}}{\sqrt{\left ( 1 - \frac{v^{2}}{c^{2}} \right )}}$
where $m_{o}$ is known as the rest mass.

(i)When v << c then, then the mass of the body $m$ equals $m_{o}$ as $1 - \frac{v^{2}}{c^{2}}$ approaches 1. Therefore, the momentum of the body is given by $\Delta p = mv$.

(ii) When v $\rightarrow$ c then $1 - \frac{v^{2}}{c^{2}}$ approaches zero. Hence, the mass of the body is variable and approaches infinity.
Therefore, the momentum of the body is given by $\Delta p = \Delta (mv)$

(b) The change in the momentum of a body depends only on the change in its velocity if the velocity of the moving body is much smaller than the velocity of light c (v << c).

Question 14 :
How is force related to the momentum of a body ?

Force is related to the momentum of a body according to Newton’s second law.

The law states that the rate of change of momentum of a body is directly proportional to the force applied on it and the change in momentum takes place in the direction of the applied force.

Mathematically, $F \propto \frac{\Delta p}{\Delta t}$
where $\Delta p$ is the change in the momentum of the body in time interval $\Delta t$

Question 15 :
State Newton’s Second law of motion. Under what condition does it take the form F = ma ?

Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the force applied on it and this change in momentum takes place in the direction of the applied force.

Mathematically, $F \propto \frac{\Delta p}{\Delta t}$
where $\Delta p$ is the change in the momentum of the body in time interval $\Delta t$

The condition under which Newton’s second law of motion takes the form F = ma are
(i) Mass of the body is constant at a velocity v
(ii) Velocity of the body is much smaller than the velocity of light, v << c

Under these conditions, the rate of change of momentum of the body is given by
$F = \frac{ \Delta p }{ \Delta t }$
$\Rightarrow F = \frac{m\Delta v}{\Delta t}$
$\Rightarrow F = m \frac{\Delta v}{\Delta t}$
$\Rightarrow F = ma$

Question 16 :
Complete the following sentences:
(a) Mass x change in velocity = ………… x time interval.
(b) The mass of a body remains constant till the velocity of the body is…………..

(a) Mass x change in velocity = …..Force….. x time interval.
(b) The mass of a body remains constant till the velocity of the body is …….much less than the velocity of light…….

Question 17 :
Prove that force = mass x acceleration. State the condition when it holds.

We know that,
the rate of change of momentum = $\frac{ \Delta p }{ \Delta t }$

When the velocity of the body is much less than the velocity of light, (v << c), then
the rate of change of momentum = $\frac{ \Delta p }{ \Delta t }$ = $m \frac{ \Delta v }{ \Delta t }$ = $ma$ ………………… (i)

From Newton’s second law of motion,
$\frac{ \Delta p }{ \Delta t } \propto F$
$\Rightarrow F \propto \frac{ \Delta p }{ \Delta t }$
$\Rightarrow F \propto ma$ …………… using (i)
$\Rightarrow F = k ma$
where k is the constant of proportionality. By choosing a suitable unit for force, the value of k is made equal to 1.
Hence, $F = ma$

The conditions under which this equation holds true are
(i) Mass of the body is constant at a velocity v
(ii) Velocity of the body (v) is much smaller than the velocity of light, v << c

Question 18 :
Name the S.I. unit of
(a) momentum
(b) rate of change in momentum

(a) The S.I. unit of momentum is kg m s -1
(b) The S.I. unit of rate of change in momentum is kg m s -2 or newton (N)

Question 19 :
State the relation between force, mass and acceleration. Draw graphs showing the relationship between
(a) Acceleration and force for a constant mass
(b) Acceleration and mass for a constant force

The relation between force, mass and acceleration is
$Force = mass\;\times\;acceleration$

Graph showing the relation between acceleration and force for a constant mass:

Graph showing the relation between acceleration and mass for a constant force:

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Published on September 7th, 2019 | by Abhishek Mandal