Question

Mark each of the following statementsas true or false. If a statement refers to "two objects"interacting via some force, you are not to assume that these twoobjects have the same mass.

Every force has one and only one 3rd law pair force.

true or false?

The two forces in each pair act in opposite directions.

true or false?

The two forces in each pair can act on the same object or ondifferent objects.

true or false?

The two forces in each pair may have different physicalorigins (for instance, one of the forces could be due to gravity,and its pair force could be a normal contact force).

true or false?

The two forces of a 3rd law pair always act ondifferent objects.

true or false?

Given that two objects interact via some force, theaccelerations of these two objects have the same magnitude butopposite directions. (Assume no other forces act on eitherobject.)

true or false?

According to Newton's 3rd law, the force on the (smaller) moondue to the (larger) earth is

greater in magnitude than, and in the oppositedirection from, the force on the earth due to the moon. greater in magnitude than, and in the samedirection as, the force on the earth due to the moon. equal in magnitude to, and in the oppositedirection from, the force on the earth due to the moon. equal in magnitude to, and in the samedirection as, the force on the earth due to the moon. smaller in magnitude than, and in the oppositedirection from, the force on the earth due to the moon. smaller in magnitude than, and in the samedirection as, the force on the earth due to the moon.

Answer 1

Concepts and reason

The required concepts to answer this question are Newton’s laws of motion. The statements are all based on Newton’s laws of motion. A good understanding of these laws is essential to understand basic mechanics.

Use Newton’s third law to answer questions based on action and reaction pair.

Use Newton’s second law to conclude the relation between force, mass and acceleration.

Fundamentals

The momentum of a body is defined as the product of mass of the body and its velocity.

The expression of the momentum is expresses as follows,

$P = mV$

Here,$P$is the momentum, $m$is the mass of the object and $V$is the velocity of the object.

Newton’s laws of motion,

1^st law: A body in state of rest or of uniform motion continues to be in the same state unless and until compelled by an external force.

2^nd law: The rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum is in the direction of force applied.

$\begin{array}{c}\\\overrightarrow F = \frac{{\left( {m{V_f} - m{V_i}} \right)}}{T}\\\\ = \frac{{m\left( {{V_f} - {V_i}} \right)}}{T}\\\end{array}$

Here,${V_f}$is the final velocity of the object and ${V_i}$is the initial velocity of the object.

Since acceleration is defined as the time rate of change of velocity, we have

$\overrightarrow F = ma$

Here,$a$is the acceleration.

3^rd law: All force between two objects exists in equal in magnitude and opposite in direction.

According to Newton’s third law, if two bodies are interacting with some force then force on these bodies can be expresses as follows,

${F_{ij}} = - {F_{ji}}$

Here, $i$ and $j$ indicate the two bodies where ${F_{ij}}$is the force on $j$body due to $i$body and${F_{ji}}$is the force on $i$body due to $j$body which is the reaction force.

From the equation we can see that there is only one reaction force.

Therefore, every force has one and only one third law pair force.

This is a True statement.

According to Newton’s third law, if two bodies are interacting with some force then force on these bodies can be written as,

${F_{ij}} = - {F_{ji}}$

Here, $i$ and $j$ indicate the two bodies where ${F_{ij}}$is the force on $j$body due to $i$body and ${F_{ji}}$is the force on $i$body due to $j$body which is the reaction force.

From the equation we can see that there is only one reaction force.

The negative sign indicates${F_{ji}}$is opposite in direction to${F_{ij}}$.

Therefore, two Forces in each pair act in opposite direction.

This is a true statement.

When two bodies are interacting, the force acting on them, according to Newton’s third law can be related as${F_{ij}} = - {F_{ji}}$.

This means the action and reaction force always act on two different bodies and never on the same body.

Therefore, the two Forces in each pair can act on same object or on different objects is a False statement.

Let’s consider gravity as an example. The earth and moon system experience action and reaction, which are both gravitational forces.

Similarly, if it is a charge influencing another charge both forces are electrical.

Every force known till date has the same property that, the two Forces in each pair can have same physical origins.

Therefore, the statement, the two Forces in each pair can have different physical origins” is False.

When two bodies are interacting, the force acting on them, according to Newton’s third law can be related as${F_{ij}} = - {F_{ji}}$.

This means the action and reaction force always act on two different bodies and never on the same body.

Therefore, the two Forces of the third law pair always act on different objects is True statement.

According to Newton’s second law we have

$F = ma$ .

Here, $\overrightarrow F$ is the force acting on the body, $m$ is the mass of the body and $a$ is the acceleration of the body.

If the force acting on two bodies is of same magnitude, the product of mass and acceleration should be of same magnitude.

The acceleration will be same in a special case where masses of both bodies are same and not always.

Therefore, the two object interact via same force, the acceleration of the two objects have same magnitude but opposite direction is False.

According to Newton’s second law we have

$F = ma$ .

Here, $\overrightarrow F$ is the force acting on the body, $m$ is the mass of the body and $a$ is the acceleration of the body.

According to Newton’s third law

Action and reaction force between earth and moon are always equal in magnitude and opposite in direction.

Therefore, we can write ${m_e}{a_e} = {m_m}{a_m}$

Here, superscript e and m indicates earth and moon respectively.

Therefore we can say the force on moon due to earth is equal in magnitude to, and in the opposite direction from, the force on the earth due to moon.

Ans:

Statement” Every Force has one and only one third law pair force” is True.