Newton's First Law: Mass and Inertia Questions in English

(C) According to Newton's first law of motion,if no net force acts on a body,it will either remain at rest or move with a constant velocity.
In a displacement-time graph,the velocity is represented by the slope of the graph.
- In region $ab$,the slope is changing (curved),indicating acceleration.
- In region $bc$,the slope is zero (horizontal),indicating the body is at rest.
- In region $cd$,the graph is a straight line,which means the slope (velocity) is constant.
- In region $de$,the slope is changing (curved),indicating acceleration.
Since the velocity is constant in region $cd$,there is no acceleration,which implies that no net force is acting on the body in this region.

(B) When a stone is rotated in a circle,it requires a centripetal force provided by the tension in the string to change its direction continuously.
According to Newton's first law of motion,an object continues to move in a straight line unless acted upon by an external force.
When the string is cut,the centripetal force (tension) becomes zero.
Due to its inertia,the stone continues to move in the direction of its velocity at that instant,which is tangent to the circular path.

(C) The correct answer is $C$. This phenomenon is based on Newton's First Law of Motion,which states that an object at rest tends to remain at rest unless acted upon by an external force.
When the horse is at rest,the rider is also at rest.
When the horse suddenly starts running,the lower part of the rider's body,which is in contact with the horse,moves forward along with the horse.
However,the upper part of the rider's body tends to remain at its state of rest due to the inertia of rest.
As a result,the upper part of the body lags behind,causing the rider to fall backward.

(C) This phenomenon is explained by Newton's First Law of Motion,which is the law of inertia.
When the train is moving,the entire body of the passenger is in a state of uniform motion.
When the train stops suddenly,the lower part of the passenger's body,which is in contact with the seat,also comes to rest due to the friction between the seat and the body.
However,the upper part of the body tends to continue its state of motion due to the inertia of motion.
As a result,the upper part of the body moves forward,causing the passengers to feel a jerk in the forward direction.

(D) . Inertia is defined as the inherent property of a body due to which it resists any change in its state of rest or of uniform motion along a straight line.
According to Newton's first law of motion,a body continues to be in its state of rest or of uniform motion unless acted upon by an external unbalanced force.
Therefore,the body is unable to change its state of rest or uniform linear motion by itself.

(B) When a person is inside a moving bus,their entire body is in a state of motion with the same velocity as the bus.
When the person steps down,their feet touch the ground and come to rest due to friction.
However,due to the inertia of motion,the upper part of the body continues to move forward at the same speed as the bus.
Consequently,the upper part of the body moves ahead of the feet,causing the person to fall forward.

(C) Newton's first law of motion defines the inertia of a body.
It states that every body has a natural tendency to remain in its state of rest or uniform motion in a straight line unless compelled to change that state by an external force.
This inherent property of a body to resist any change in its state is known as inertia.

(D) According to Newton's First Law of Motion,an object in motion will continue to move with a constant velocity in a straight line unless acted upon by an external unbalanced force.
Since the particle is already moving with a constant speed along a straight line,it possesses uniform velocity.
Therefore,no external force is required to maintain this state of motion.
Options $A$,$B$,and $C$ involve changing the state of motion (acceleration),which requires a force.

(A) According to the law of inertia of motion,a body will continue moving with constant velocity unless an external force acts on it.
When a bus is moving straight,the passengers inside are also moving in a straight line.
When the bus suddenly turns,the passengers tend to continue moving in their original straight-line path due to their inertia of motion.
Since no immediate force acts on the passengers to change their direction of motion along with the bus,they appear to be thrown outwards relative to the bus.

(B) According to Newton's First Law of Motion,an object remains in a state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force. If the resultant force acting on an object is zero,the object will continue to move with a constant velocity (uniform motion). Therefore,the condition for uniform motion is that the resultant force must be zero.

(A) According to Newton's First Law of Motion,an object will maintain its state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.
Given that all forces acting on the aircraft are balanced,the net force $F_{net} = 0$.
From Newton's Second Law,$F_{net} = ma$. Since $F_{net} = 0$,the acceleration $a = 0$.
An acceleration of zero implies that the velocity of the aircraft remains constant.
Therefore,the aircraft will continue to move with the same velocity of $300\,m/s$ in a straight line.

(A) According to Newton's first law of motion,an object continues to be in its state of rest or of uniform motion in a straight line unless compelled by an external force to change that state.
When a car moves at high speed and takes a sharp turn,the car changes its direction of motion.
However,the driver,due to the property of inertia of direction,tends to continue moving in the original straight-line path.
As the car turns away from this straight path,the driver feels a force pushing them towards the side opposite to the turn relative to the car's frame of reference.
Therefore,this phenomenon is due to the inertia of direction.

(A) When the girl jumps from a moving bus,her entire body possesses the velocity of the bus due to the inertia of motion.
When her feet touch the ground,they experience a retarding force.
In case $(b)$,the patch of glue provides a large frictional force,bringing her feet to an immediate stop,while her upper body continues to move forward due to inertia,causing her to fall forward.
In case $(a)$,the sheet of ice provides very little friction. Her feet continue to slide forward along with the rest of her body,which helps her maintain balance or at least prevents the sudden stop that causes a forward fall. However,if she does fall,the inertia of motion still acts on her upper body,and she will still tend to fall forward if her feet are obstructed or if she loses balance,but the effect is most pronounced in case $(b)$. Given the standard physics problem context,in both scenarios,the inertia of motion causes a forward tendency; thus,she falls forward in both cases.

(A) When the person tosses the coin,the coin shares the horizontal velocity of the train.
If the train moves with a uniform velocity,the coin will fall back into the person's hand due to the principle of inertia.
However,if the train is accelerating forward,the train gains more velocity while the coin is in the air.
Since the coin maintains its initial horizontal velocity (due to inertia),the train moves ahead of the coin,causing the coin to fall behind the person.
Therefore,the train is moving forward and gaining speed.

(B) An inertial frame of reference is one that is either at rest or moving with a constant velocity (zero acceleration).
In option $A$,the child is in circular motion,which involves centripetal acceleration.
In option $B$,the sports car is moving with a constant speed on a straight road,meaning its velocity is constant and its acceleration is zero. Thus,the driver is in an inertial frame.
In option $C$,the aeroplane is taking off,meaning it is accelerating.
In option $D$,the cyclist is turning,which involves centripetal acceleration.
Therefore,only the observer in option $B$ is in an inertial frame.

(A) Newton's first law of motion states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
This law defines force as that which changes the state of rest or uniform motion of an object.
It implies that force is an external agent that can exist independently of the object's motion,establishing the concept of the physical independence of force.
Therefore,the first law of motion is the basis for the physical independence of force.

(B) An inertial frame is a frame of reference that is either at rest or moving with a constant velocity (zero acceleration).
In option $A$,the child is in circular motion,which involves centripetal acceleration.
In option $B$,the car is moving with a constant speed on a straight road,meaning its velocity is constant and its acceleration is zero. Therefore,it acts as an inertial frame.
In option $C$,the aeroplane is accelerating during takeoff.
In option $D$,the cyclist is changing direction,which involves acceleration.
Thus,the driver in the sports car is the correct observer in an inertial frame.

(C) An inertial frame of reference is defined as a frame in which Newton's laws of motion are valid.
Since the vehicle is moving with a constant speed on a straight road,its acceleration is $0$. Therefore,it is an inertial frame of reference.
Thus,the $Assertion$ is correct.
However,the $Reason$ states that a frame where Newton's laws are applicable is non-inertial,which is false. Newton's laws are applicable in inertial frames,not non-inertial frames.
Therefore,the $Assertion$ is correct but the $Reason$ is incorrect.

(A) According to Newton's first law of motion,an object remains in its state of rest or uniform motion in a straight line unless acted upon by an external force.
Once the astronaut is separated from the spaceship,there are no external forces acting on him because there are no nearby stars to exert gravitational force,and the gravitational pull of the small spaceship is negligible.
Since the net external force $F_{net} = 0$,the acceleration $a = F_{net}/m$ must also be $0$.
Therefore,the acceleration of the astronaut the instant after he is outside the spaceship is $0 \; m/s^2$.

(D) The trolley and the sandbag constitute a system moving on a frictionless track.
Since there is no external horizontal force acting on the system,the net external force is zero.
According to Newton's first law of motion,an object in motion will continue to move with the same velocity unless acted upon by an external force.
The leaking of sand is an internal process within the system and does not exert any external force on the trolley.
Therefore,the velocity of the trolley remains constant throughout the process.
Thus,the speed of the trolley after the sandbag is empty remains $27 \; km/h$.

(N/A) $(1)$ Dynamics: The branch of physics that describes the motion of objects along with its causes (forces) is known as Dynamics.
$(2)$ Mechanics: The branch of physics which studies and deals with the motion of objects is called Mechanics. Alternatively,Kinematics and Dynamics are combinedly known as Mechanics.

(N/A) The differences between mass and weight are summarized in the table below:

Mass	Weight
$1$. It is the quantity of matter contained in a body. It is denoted by $m$.	$1$. It is the gravitational force acting on a body. It is denoted by $W$.
$2$. It is a scalar and fundamental physical quantity.	$2$. It is a vector and derived physical quantity.
$3$. The mass of an object can never be zero.	$3$. The weight of an object can be zero. At the center of the Earth,$g = 0$,so the weight is zero.
$4$. Its $SI$ unit is $kg$.	$4$. Its $SI$ unit is $newton$ $(N)$.
$5$. Mass remains constant everywhere.	$5$. Weight varies from place to place.

(B) When a stone is whirled in a circular path,its velocity vector is always directed along the tangent to the circle at any given point.
When the string breaks,the centripetal force,which was responsible for keeping the stone in circular motion,vanishes.
According to Newton's First Law of Motion,an object in motion continues to move in a straight line at a constant velocity unless acted upon by an external force. Therefore,due to the inertia of direction,the stone continues to move along the tangent at the point where the string broke.

(N/A) To bring a stationary object into motion,a force is required. Similarly,to slow down an object in motion or to stop a moving object,a force is required.
$A$ ball is moving down along a slope. By applying a force in the opposite direction,it can be stopped. The external parameter (agency) by which the state of motion or rest can be changed is called force.
The effects of force on a body can be the following:
$(i)$ Force can bring a body from rest to motion or a body from motion to rest.
$(ii)$ It can increase or decrease the speed of an object.
$(iii)$ Force can change the direction of motion of an object.
$(iv)$ Force can change the shape of an object.

(N/A) Greek philosopher Aristotle,based on his observations of daily life,assumed that an external agency (force) is required to maintain the uniform motion of a body. This is known as Aristotle's law of motion. According to him,an arrow released from a bow continues its motion because the air behind the arrow pushes it forward.
Aristotle's mistake was that he treated practical experience as a fundamental law of nature. In reality,frictional forces oppose the motion of solid objects,and viscous forces oppose the motion of fluids. He failed to account for these resistive forces. His flaw was the assumption that a force is needed to sustain motion,whereas,in reality,a force is only required to overcome resistive forces to maintain uniform motion.

(N/A) Aristotle's law of motion states that an external force is required to keep a body in motion. According to this view,if a body is moving,it will come to rest as soon as the external force acting on it is removed. In modern physics,this is understood to be incorrect because it ignores the effect of friction,which is the actual force that brings moving objects to rest on Earth.

(N/A) Aristotle's fundamental mistake was the assumption that an external force is required to keep a body in a state of uniform motion. According to Aristotle,if a body is moving,it must be pushed by an external agent to maintain its velocity. He failed to account for the role of friction and air resistance,which are the actual forces that bring a moving object to rest in real-world scenarios. In the absence of such resistive forces,an object in motion will continue to move with a constant velocity indefinitely,as stated by Newton's First Law of Motion.

(B) The mass of a body is a quantitative measure of its inertia.
Inertia is the property of a body by virtue of which it resists any change in its state of rest or uniform motion in a straight line.
Therefore,a body with greater mass has greater inertia,meaning it is harder to change its state of motion.

(N/A) Galileo's law of inertia was the basis of Newton's laws of motion.
Newton's first law of motion: Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.
$A$ body at rest or a body moving with constant velocity both represent zero acceleration. Hence,Newton's first law can be interpreted as follows:
Force is a physical quantity which can bring a body at rest into motion and which can change the velocity of an object.
In short,the physical quantity which can produce acceleration in a body is called force.
From Newton's first law,the magnitude of force cannot be determined. This is its limitation.

(B) The statement is False.
When a body is at rest or in uniform motion,it does not mean that no force acts on it. Rather,it means that the net (resultant) external force acting on the body is zero.
For example,consider a book at rest on a horizontal table:
$(1)$ The gravitational force (weight,$W = mg$) acts on the book in the downward direction.
$(2)$ The normal force $(N)$ exerted by the table acts on the book in the upward direction.
Since the book is at rest,by Newton's first law of motion,the net force must be zero. Therefore,the normal force and the weight must be equal in magnitude and opposite in direction $(N = W)$.
Thus,multiple forces act on the body,but their vector sum is zero.

(N/A) According to Newton's First Law of Motion, an object remains in a state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.
If a car is moving with a constant (uniform) velocity, its acceleration $(a)$ is zero.
According to Newton's Second Law of Motion, the resultant force $(F_{net})$ acting on an object is given by $F_{net} = m \cdot a$.
Since the velocity is constant, the acceleration $a = 0$. Therefore, $F_{net} = m \cdot 0 = 0$.
This means that the vector sum of all external forces acting on the car (such as the driving force from the engine, air resistance, and rolling friction) must be zero for the car to maintain a constant velocity.

(N/A) When we are standing in a stationary bus,our feet are in contact with the floor. There is a frictional force between our feet and the floor of the bus.
When the bus suddenly starts,due to friction,our feet start moving in the direction of the bus,whereas the rest of our body tries to retain its position due to inertia of rest.
Hence,we are thrown in the backward direction,which is opposite to the direction of the acceleration of the bus.

(B) When the bus is moving with a constant velocity,our body is also in a state of motion along with the bus.
According to Newton's First Law of Motion,an object in motion will continue to remain in motion unless acted upon by an external force.
When the brakes are applied,the bus comes to a state of rest,but our body,due to the inertia of motion,tends to continue moving forward.
Therefore,we experience a jerk in the forward direction.

(N/A) Inertia is the inherent property of a body by virtue of which it resists any change in its state of rest or uniform motion in a straight line.
It is a measure of the mass of an object; the greater the mass,the greater the inertia.
There are three types of inertia: inertia of rest,inertia of motion,and inertia of direction.

(A) According to Newton's second law of motion,$F = ma$.
If the acceleration $a$ is to be kept constant,then the force $F$ is directly proportional to the mass $m$ $(F \propto m)$.
Therefore,a heavier object (having larger mass $m$) requires a larger force $F$ to achieve the same acceleration $a$.

(B) The property of an object by virtue of which it resists any change in its state of rest or uniform motion in a straight line is called $Inertia$. $Inertia$ is a measure of the mass of the body; the greater the mass,the greater the $Inertia$.

(N/A)

Mass	Weight
$1$. Mass is the quantity of matter contained in a body.	$1$. Weight is the gravitational force acting on a body.
$2$. It remains constant at all places.	$2$. It varies from place to place.
$3$. It is a scalar quantity.	$3$. It is a vector quantity.
$4$. Its $SI$ unit is $kg$.	$4$. Its $SI$ unit is $kg \cdot m/s^2$ (Newton).

(N/A) When a person driving a car suddenly applies the brakes,the lower part of the body,which is in contact with the seat,slows down along with the car due to the frictional force.
However,the upper part of the body continues to move forward due to the $inertia$ $of$ $motion$.
Since the person is not wearing a seat belt,there is no external force to stop the forward motion of the upper body,causing them to fall forward and hit their head against the steering wheel.

(B) When the lower thread $CD$ is pulled with a sudden jerk,the force applied is impulsive and acts only on the lower thread $CD$.
Due to the inertia of the $2\, kg$ mass,it does not immediately move downwards to transmit the force to the upper thread $AB$.
As a result,the tension in the lower thread $CD$ exceeds its breaking strength almost instantaneously,causing it to break.
The upper thread $AB$ remains unaffected because the force does not have enough time to be transmitted to it.
Therefore,the correct option is $B$.

(N/A) Yes,it is possible. Inertia is a property of a body determined by its mass $(m)$,which is an intrinsic property and remains constant regardless of the location. Weight $(W = mg)$ is the force exerted by gravity on the body. At the centre of the Earth,the gravitational acceleration $(g)$ becomes zero. Therefore,a body placed at the centre of the Earth will have mass (and thus inertia) but its weight will be zero.

(B) The correct answer is $(B)$.
When an athlete is running,their body is in a state of uniform motion.
According to Newton's First Law of Motion,an object in motion will continue to remain in motion unless acted upon by an external force.
Therefore,due to the inertia of motion,the athlete cannot come to rest immediately upon crossing the winning line,as their body tends to maintain its state of motion.

(B) Newton's first law of motion states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
This law is valid only in inertial reference frames,which are frames of reference that are not accelerating.
In non-inertial reference frames,pseudo-forces appear,and the law does not hold in its standard form.
Therefore,the correct option is $B$.

(B) According to Newton's First Law of Motion,an object in motion will continue to move with a constant velocity in a straight line unless acted upon by an external unbalanced force.
Since the body is moving with a constant velocity of $4 \, m/s$ on a frictionless surface,there is no acceleration $(a = 0)$.
Using Newton's Second Law,$F = ma$.
Substituting the values,$F = 2 \, kg \times 0 \, m/s^2 = 0 \, N$.
Therefore,no external force is required to maintain the constant velocity.

(D) To determine the motion of the object,we calculate the resultant force $\vec{F}_{net}$ acting on it.
Given forces are $\vec{F}_1 = 2 \hat{i} + 2 \hat{j}$,$\vec{F}_2 = 2 \hat{i} - 2 \hat{j}$,and $\vec{F}_3 = -4 \hat{i}$.
The resultant force is $\vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3$.
$\vec{F}_{net} = (2 \hat{i} + 2 \hat{j}) + (2 \hat{i} - 2 \hat{j}) + (-4 \hat{i})$.
$\vec{F}_{net} = (2 + 2 - 4) \hat{i} + (2 - 2) \hat{j} = 0 \hat{i} + 0 \hat{j} = 0$.
Since the net force acting on the object is zero,the object remains in its state of rest according to Newton's first law of motion.
Therefore,the object does not move.

(C) An inertial frame of reference is one that is either at rest or moving with a constant velocity (zero acceleration).
Since the Earth revolves around the Sun and rotates about its own axis,it possesses centripetal acceleration in both cases.
Because the Earth is an accelerating frame,any reference frame attached to it is non-inertial.
Therefore,both the revolution of the Earth around the Sun and the rotation of the Earth about its axis contribute to it being a non-inertial frame.
Thus,the correct option is $C$.

(B) Assertion $A$ is correct because an electric fan has rotational inertia. When the power is switched off,the fan does not stop instantly due to its inertia of motion,which resists the change in its state of rotation.
Reason $R$ is also correct because the tendency of a body to maintain its state of motion is defined as the inertia of motion. Therefore,the fan continues to rotate because of this property.
Since $R$ correctly explains why the fan continues to rotate after the power is cut,$R$ is the correct explanation of $A$.

(B) $Statement-1$ is True because of the property of inertia. When the cloth is pulled out very quickly,the time interval for the force to act on the dishes is extremely small. Due to the inertia of rest,the dishes tend to remain in their position.
$Statement-2$ is a fundamental law of motion (Newton's Third Law),which is also True. However,the phenomenon of pulling the cloth without moving the dishes is explained by Newton's First Law (Inertia),not the Third Law.
Therefore,$Statement-2$ is not the correct explanation for $Statement-1$.

(A) According to Newton's first law of motion,an object will maintain its state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.
Since all the forces acting on the aircraft are balanced,the net force $(F_{net})$ acting on it is $0 \ N$.
Therefore,the aircraft will continue to move with the same uniform velocity of $150 \ m/s$ without any change in its speed or direction.

(C) An inertial frame of reference is a frame that is either at rest or moving with a constant velocity (zero acceleration).
In option $A$,the train is slowing down,meaning it has a non-zero acceleration (deceleration).
In option $B$,the child is revolving,which involves a change in direction,meaning there is centripetal acceleration.
In option $C$,the bus is moving with a constant velocity,which implies zero acceleration. Therefore,this is an inertial frame of reference.
In option $D$,the aeroplane is taking off,which involves changing speed and direction,meaning it has non-zero acceleration.
Thus,the correct option is $C$.