The law of inertia MCQ Quiz - Objective Question with Answer for The law of inertia - Download Free PDF

The correct answer is Your body.

Concept:

Newton’s First Law: It states that a body continues in its state of rest or uniform motion in a straight line until and unless an unbalanced force acts on it.

• Newton’s First Law is also known as the law of inertia.
• Inertia is the property of the inability of a body to change its position of rest or uniform motion in a straight line.
• It is valid only in an inertial frame.
• Mass is the measure of the inertia of a body.
• The higher the mass of the body, the higher would be its inertia.

Key Points

• Hence amongst the following options, the human body has the highest mass thus it has the highest inertia.
• Inertia is a property of an object to resist changes in its current state of motion and is directly proportional to the mass of the object.
• Mass is solely dependent upon the inertia of the object.
• Higher the inertia more mass the body will have and vice versa.
• A heavier object has a higher tendency to resist changes in its state of motion.

CONCEPT:

Inertia

• Inertia is the property of an object to resist changes in its state of motion. It is directly related to the mass of the object.
• The greater the mass of an object, the greater its inertia. This is because heavier objects require more force to change their motion compared to lighter objects.

EXPLANATION

• A cycle has the least mass among the options, so it has the least inertia.
• A scooter has more mass than a cycle, so it has slightly higher inertia.
• A car is heavier than a scooter and cycle, so its inertia is higher.
• A truck has the highest mass among all the given options, making its inertia the highest.

Inertia is directly proportional to the mass of the object. Since the truck has the greatest mass, it has the highest inertia.

Therefore, the correct answer is Truck.

The correct answer is \(\frac{MR^2}{4}\)

Concept:

• Moment of Inertia: Moment of inertia plays the same role in rotational motion as mass plays in linear motion. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation.
• And the moment of inertia of a particle is given as I = MR2

Perpendicular axis theorem: This theorem states that the moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with the perpendicular axis and lying in the plane of the body.

Hence it can be expressed as \({I_z} = {I_y} + {I_x}\)

Here Ix, Iy and Iz are the moment of inertia of an object along X, Y and Z- axis respectively

Explanation:

Now the moment of inertia of a disc about an axis through its centre of mass = \({I_{CM}} = \frac{1}{2}M{R^2}\)

And according to the given condition if the given disc is rotated about one of its diameters

Hence its rotation can be either along X-axis or Y-axis and the Centre of mass will be situated at the origin as shown below

From this, we can see that Ix = Iy , since the disc is uniform and it doesn’t matter if it's rotated along any of the diameters its moment of inertia will be the same i.e., ID = Ix = Iy

Now by using perpendicular axis theorem IZ = Ix + IY = 2ID

And since the Centre of the mass of the given disc is situated at the origin, Iz = IC.M = ½ MR2

∴ \({I_Z} = \frac{1}{2}M{R^2} = 2{I_D} \Rightarrow {I_D} = \frac{{M{R^2}}}{4}\)

 Important Points

This is a moment of inertia of a circular disc about the different axis of rotation

 Explanation:

When a car is moving forward and suddenly brakes , the objects inside the car tend to maintain their motion due to inertia (Newton’s First Law of Motion).

The liquid inside the cup is not rigidly attached to the cup and will continue moving forward relative to the ground. However, the cup experiences the braking force applied by the car.

The cup slows down along with the car because it is in contact with it.

The liquid inside does not experience the same immediate braking force.

As a result, the liquid appears to move backward relative to the cup .

Correct Option: Option 2 

Key Points

• Inertia is the property of a body to resist any change in its state of motion or rest.
• When a bus suddenly applies brakes, the lower part of the passenger's body, which is in contact with the bus, tends to come to rest with the bus.
• However, the upper part of the body continues to move forward due to inertia, making the passenger bend forward.
• This phenomenon is a direct consequence of Newton's First Law of Motion, which states that an object will remain in its state of rest or uniform motion unless acted upon by an external force.

Additional Information

• Newton's First Law of Motion (Law of Inertia):
  • This law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
  • It explains the concept of inertia, which is the tendency of an object to resist changes to its state of motion.
• Inertia:
  • It is a property of matter that causes it to resist changes in its state of motion or rest.
  • There are three types of inertia:
    • Inertia of Rest: The tendency of a body to remain at rest unless acted upon by an external force.
    • Inertia of Motion: The tendency of a body to continue in its state of uniform motion unless acted upon by an external force.
    • Inertia of Direction: The tendency of a body to continue moving in the same direction unless acted upon by an external force.
• Momentum:
  • Momentum is the product of the mass and velocity of an object.
  • It is given by the formula: Momentum (p) = Mass (m) × Velocity (v).
  • While momentum is related to motion, it is not the primary cause of the passenger bending forward in this case.
• Gravity:
  • Gravity is the force of attraction between two objects due to their masses.
  • In this question, gravity is not responsible for the forward motion of the passenger.
• Pressure:
  • Pressure is the force exerted per unit area.
  • It is unrelated to the phenomenon described in the question.

The correct answer is Your body.

Concept:

Newton’s First Law: It states that a body continues in its state of rest or uniform motion in a straight line until and unless an unbalanced force acts on it.

• Newton’s First Law is also known as the law of inertia.
• Inertia is the property of the inability of a body to change its position of rest or uniform motion in a straight line.
• It is valid only in an inertial frame.
• Mass is the measure of the inertia of a body.
• The higher the mass of the body, the higher would be its inertia.

Key Points

• Hence amongst the following options, the human body has the highest mass thus it has the highest inertia.
• Inertia is a property of an object to resist changes in its current state of motion and is directly proportional to the mass of the object.
• Mass is solely dependent upon the inertia of the object.
• Higher the inertia more mass the body will have and vice versa.
• A heavier object has a higher tendency to resist changes in its state of motion.

The correct answer is Inertia is measured in kilo grams. 

CONCEPT:

Inertia 

• An inherent property of all the bodies by virtue of which they cannot change their state of rest or uniform motion along a straight line by their own is called inertia.
• Inertia is not a physical quantity, it is only a property of the body which depends on the mass of the body.
• Inertia has no units and no dimensions.

EXPLANATION:

• Inertia is related to mass but it is not a physical quantity.
• From the above, it is clear that the property of the body which depends on the mass of the body i.e., the mass of an object is a measure of its inertia.
• SI unit of mass is the kilogram (kg). Therefore option 4 is correct.

The correct answer is option 1) i.e. Newton's first law of motion

CONCEPT:

• Newton's first law of motion: It states that an object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.
  • This means that the object at rest would have a tendency to stay at rest and an object in motion will have a tendency to stay in motion.
  • This law is also known as the law of inertia.
• ​Newton's second law of motion: It states that the rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force.
• Newton's third law of motion: It states that for every action, there must be an equal and opposite reaction.

EXPLANATION:

• ​Since the law of inertia follows Newton's first law of motion so the correct answer is option 1.

Stone has greater inertia.

EXPLANATION:

• Inertia is directly proportional to Mass. 
• If the mass is high then the inertia is also high and vice versa is also true.
• Since the mass of the stone is more than the mass of the man. So the stone has greater inertia. Hence option 2 is correct.

Additional Information

• Inertia is the ability of a body by virtue of which it opposes a change.
• According to Newton’s first law of motion, an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
  • The inertia of rest: When a body is in rest, it will remain at rest until we apply an external force to move it. This property is called inertia of rest.
  • The inertia of motion: When a body is in a uniform motion, it will remain in motion until we apply an external force to stop it. This property is called inertia of motion.​

The correct answer is \(\frac{MR^2}{4}\)

Concept:

• Moment of Inertia: Moment of inertia plays the same role in rotational motion as mass plays in linear motion. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation.
• And the moment of inertia of a particle is given as I = MR2

Perpendicular axis theorem: This theorem states that the moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with the perpendicular axis and lying in the plane of the body.

Hence it can be expressed as \({I_z} = {I_y} + {I_x}\)

Here Ix, Iy and Iz are the moment of inertia of an object along X, Y and Z- axis respectively

Explanation:

Now the moment of inertia of a disc about an axis through its centre of mass = \({I_{CM}} = \frac{1}{2}M{R^2}\)

And according to the given condition if the given disc is rotated about one of its diameters

Hence its rotation can be either along X-axis or Y-axis and the Centre of mass will be situated at the origin as shown below

From this, we can see that Ix = Iy , since the disc is uniform and it doesn’t matter if it's rotated along any of the diameters its moment of inertia will be the same i.e., ID = Ix = Iy

Now by using perpendicular axis theorem IZ = Ix + IY = 2ID

And since the Centre of the mass of the given disc is situated at the origin, Iz = IC.M = ½ MR2

∴ \({I_Z} = \frac{1}{2}M{R^2} = 2{I_D} \Rightarrow {I_D} = \frac{{M{R^2}}}{4}\)

 Important Points

This is a moment of inertia of a circular disc about the different axis of rotation

CONCEPT:

Inertia:

• The tendency of the body to oppose the change in its state of rest or uniform motion in a straight line is called inertia.
• Newton's first law of motion is also called the law of inertia.
• Inertia depends upon mass. If the mass is more the inertia will also be more.

EXPLANATION:

• When a bullet is fired from a gun and it strikes on the glass of a window, a small hole will be generated on the window because the bullet strikes the window at the very small portion and makes it get into motion for a very short time due to its high speed whereas the remaining portion of the window remains at rest due to inertia of rest. Hence, option 1 is correct.

The correct answer is option 2) i.e. Move forward

CONCEPT:

• ​Inertia is the property of an object by virtue of which it opposes any event that attempts to put the object in motion or to change its velocity. 
  • Therefore, an object at rest would want to continue staying at rest and an object in motion would have a tendency to continue its motion.
  • Greater the mass of the object more will be the tendency to resist the events.
• Newton's first law of motion: It states that an object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.
  • This law is also known as the law of inertia.

EXPLANATION:

• As the truck is moving forward with a constant velocity, the tank along with the water is also moving under constant velocity.
• When a sudden brake is applied, it tends to oppose the forward motion of water in the tank.
• Due to the inertia of water, it would have a tendency to continue its forward motion. Hence on sudden braking, it suddenly moves forward.

CONCEPT:

• The law of inertia says that If an object is at rest it remains at rest, or if in motion, remains in motion at a constant velocity unless an external force acts on it.
• The greater the mass, the more is the inertia of motion of the body.

EXPLANATION:

• Since inertia of a body is related to the mass of a body.
• If a body has more mass, it will have a tendency to remain at rest for more time than less mass.
• So more mass means more inertia.
• Hence inertia of motion of a body depends on the mass.
• So the correct answer is option 1.

Concept:

Moment of inertia:

• The moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
• The moment of inertia of a particle is

⇒ I mr2

Where r = the perpendicular distance of the particle from the rotational axis.

Explanation:

Given that, BC = 2AB

\( {I_{BC}} = \frac{{M{{(AB)}^2}}}{3} = \frac{{m{a^2}}}{3}\)

\( i.e\;AB = a = \frac{{BC}}{2} \)

\( Moment\:of\:inertia\:at\:AB,{I_{AB}} = \frac{{m{{(BC)}^2}}}{3} = \frac{{M{{(2a)}^2}}}{3} = \frac{{4m{a^2}}}{3} \)

\( Moment\:of\:inertia\:at\:HF,{I_{HF}} = \frac{{m{{(AB)}^2}}}{{12}} = \frac{{m{a^2}}}{{12}} \)

\(Moment\:of\:inertia\:at\:EG,{I_{EG}} = \frac{{m(BC)}}{{12}} = \frac{{m{a^2}}}{{12}} \)

The moment of inertia is minimum about EG because mass distribution is at the minimum distance from EG

The correct answer is By its mass.

• There is a resistance offered by an object to change its state of motion. If it is at rest it tends to remain at rest; if it is moving it tends to keep moving.
• This property of an object is called its inertia.
• A force that is just enough to cause a small cart to pick up a large velocity will produce a negligible change in the motion of a train.
  • This is because in comparison to the cart the train has a much lesser tendency to change its state of motion.
• Accordingly, we say that the train has more inertia than the cart.
• Clearly, heavier or more massive objects offer larger inertia.
• Quantitatively, the inertia of an object is measured by its mass.