Mix Example - FORCE AND LAWS OF MOTION Questions in English

(A) An object moving in an accelerated motion along a straight path must have a changing velocity,which implies that its speed may change or its direction of motion might change (though in a straight line,only speed changes). According to Newton's $Second$ $Law$ of $Motion$,an acceleration requires a net external force to act on the object. Therefore,options $B$,$C$,and $D$ are correct characteristics of accelerated motion. Option $A$ is incorrect because an object moving in an accelerated motion along a straight path does not necessarily move away from the earth; it could be moving towards the earth or horizontally.

(B) According to Newton's third law of motion,for every action,there is an equal and opposite reaction.
These two forces always act on two different bodies.
They are equal in magnitude and opposite in direction.

(C) According to Newton's second law of motion,the force exerted is given by $F = \frac{\Delta p}{\Delta t}$,where $\Delta p$ is the change in momentum and $\Delta t$ is the time taken.
By pulling his hands backwards,the goalkeeper increases the time $(\Delta t)$ taken to bring the ball to rest.
Since the force is inversely proportional to time,increasing the time interval reduces the impact force exerted by the ball on the goalkeeper's hands,thereby preventing injury.

(D) Inertia is defined as the inherent property of a body by virtue of which it opposes or resists any change in its state of rest or uniform motion in a straight line.
According to Newton's first law of motion,an object will remain at rest or continue to move at a constant velocity unless acted upon by an external unbalanced force.
Therefore,inertia is the tendency of an object to resist any change in its state of motion.

(A) According to the law of inertia,the coin and the passenger are moving with the same initial velocity as the train. When the coin is tossed,it maintains its horizontal velocity due to inertia. If the train were moving with uniform velocity,the coin would fall back into the passenger's hand. If the train were decelerating (retarded),the train would slow down while the coin continues at the higher initial velocity,causing the coin to fall in front of the passenger. Since the coin falls behind the passenger,the train must be accelerating,meaning the train's velocity increases while the coin is in the air,leaving the passenger ahead of the coin's landing position.

(B) According to Newton's first law of motion,an object in uniform motion will continue to move with the same velocity unless acted upon by an external unbalanced force.
Since the table is frictionless and the object is moving with a constant velocity,there is no opposing force (like friction) acting on it.
Therefore,no external force is required to maintain its state of motion.
Thus,the force required is $0\, N$.

(C) rocket operates based on Newton's $3^{rd}$ law of motion and the principle of conservation of linear momentum.
As the fuel burns,the rocket expels hot gases at high velocity in the downward direction.
According to the law of conservation of momentum,the total momentum of the system (rocket + gases) remains constant in the absence of external forces.
Since the gases gain momentum in the downward direction,the rocket gains an equal and opposite momentum in the upward direction,which provides the necessary thrust for the rocket to lift off.

(D) According to Newton's first law of motion,an object in motion continues to be in motion unless acted upon by an external force.
When the tanker is moving at a uniform speed,the water inside it is also moving at the same speed.
When the brakes are applied suddenly,the tanker comes to rest,but the water inside continues to be in a state of motion due to inertia.
Therefore,the water in the tank would move forward.

(B) Inertia is directly proportional to the mass of an object $(I \propto m)$.
Since all three solids have the same shape and volume,their masses depend on their densities $(m = \rho \times V)$.
Among aluminium,steel,and wood,steel has the highest density.
Therefore,the steel solid will have the greatest mass.
Since it has the greatest mass,it will possess the highest inertia.

(N/A) Yes,the balls will start rolling in the direction in which the train was moving.
Due to the application of the brakes,the train comes to rest,but due to the property of inertia,the balls try to remain in their state of motion; therefore,they begin to roll forward.
Since the masses of the rubber and iron balls are different,their inertia of motion is different.
Consequently,the inertial forces acting on them are not the same,and they will move with different speeds.

(A) According to the law of conservation of momentum,the momentum of the bullet is equal to the momentum of the rifle $(p = mv)$.
Since the force applied is the same,the impulse $(F \times t)$ imparted to both rifles is the same,resulting in the same change in momentum.
For a light rifle,the mass $(m)$ is smaller,so to achieve the same momentum,the recoil velocity $(v)$ must be significantly higher.
For a heavy rifle,the mass $(m)$ is larger,resulting in a lower recoil velocity $(v)$.
Since the kinetic energy of recoil $(KE = \frac{1}{2}mv^2)$ is proportional to the square of the velocity,the lighter rifle experiences a higher recoil velocity,which causes a greater impact force on the shoulder. Therefore,the lighter rifle will hurt the shoulder more.

(N/A) When a cart moves on the road,it encounters frictional force between the wheels and the ground.
According to Newton's first law of motion,an object in motion will continue to move at a constant velocity only if the net external force acting on it is zero.
Since friction acts as an opposing force that tends to slow down the cart,the horse must apply an external force equal and opposite to the frictional force to maintain a net force of zero.
Therefore,the horse continues to apply a force to overcome friction and maintain a constant speed.

(N/A) The Law of Conservation of Momentum is applicable only to an isolated system where no external force acts on the system.
In this case,the ball is not an isolated system because it is constantly acted upon by the external gravitational force of the Earth.
This external force causes a change in the velocity and,consequently,the momentum of the ball.
Therefore,since an external force is present,the momentum of the ball alone is not conserved.

(N/A) Given:
Mass of the ball,$m = 50 \, g = 0.05 \, kg$
Initial velocity,$u = 80 \, m \, s^{-1}$ (at $t = 0 \, s$)
Final velocity,$v = 0 \, m \, s^{-1}$ (at $t = 8 \, s$)
Time taken,$t = 8 \, s$
$1$. Calculation of acceleration $(a)$:
$a = \frac{v - u}{t} = \frac{0 - 80 \, m \, s^{-1}}{8 \, s} = -10 \, m \, s^{-2}$
The negative sign indicates retardation (deceleration).
$2$. Calculation of frictional force $(F)$:
$F = m \times a$
$F = 0.05 \, kg \times (-10 \, m \, s^{-2}) = -0.5 \, N$
The negative sign indicates that the frictional force acts in the direction opposite to the motion of the ball.

(C) According to Newton's second law of motion,the acceleration $a$ is given by $a = \frac{F}{m}$.
Initially,the acceleration of the truck is $a_1 = \frac{F}{M}$.
When the truck is loaded with an object of mass equal to the truck,the new mass becomes $M' = M + M = 2M$.
The driving force is halved,so the new force becomes $F' = \frac{F}{2}$.
The new acceleration $a_2$ is given by $a_2 = \frac{F'}{M'} = \frac{F/2}{2M} = \frac{F}{4M}$.
Comparing the new acceleration with the initial acceleration: $\frac{a_2}{a_1} = \frac{F/4M}{F/M} = \frac{1}{4}$.
Therefore,the acceleration becomes one-fourth of its original value.

(N/A) The separation between them will increase.
Initially,the momentum of both friends is zero as they are at rest.
According to the law of conservation of momentum,when the first person throws the ball,they must move in the opposite direction to the ball to conserve momentum.
When the second person catches the ball,they receive the momentum of the ball,which causes them to move backward in the direction of the ball's motion.
Consequently,both friends move away from each other,increasing the distance between them.

(N/A) The rotation of the water sprinkler is based on Newton's $Third$ Law of Motion.
When water is supplied, it rushes out through the nozzles of the sprinkler at a high velocity.
According to Newton's $Third$ Law of Motion, for every action, there is an equal and opposite reaction.
The water exerts an action force on the nozzle in the backward direction, and the nozzle exerts an equal and opposite reaction force on the water.
Due to this reaction force, the sprinkler arm experiences a torque that causes it to rotate in the opposite direction of the water flow.

(B) Derivation: According to Newton's second law,$F \propto \frac{dp}{dt}$. Since $p = mv$,$F = k \frac{d(mv)}{dt} = kma$. Taking $k=1$,we get $F = ma$.
$(i)$ Given: $m = 10 \, g = 0.01 \, kg$,$u = 10^3 \, m \, s^{-1}$,$v = 0$,$s = 5 \, cm = 0.05 \, m$.
Using $v^2 - u^2 = 2as$:
$0^2 - (10^3)^2 = 2 \cdot a \cdot 0.05$
$-10^6 = 0.1 \cdot a$
$a = -10^7 \, m \, s^{-2}$.
Resistive force $F = |ma| = 0.01 \times 10^7 = 10^5 \, N$.
$(ii)$ Using $v = u + at$:
$0 = 10^3 + (-10^7) \cdot t$
$10^7 \cdot t = 10^3$
$t = 10^{-4} \, s$.

(C) According to Newton's second law of motion,$F = ma$. The $SI$ unit of force is $kg \, m s^{-2}$,which is defined as $1 \, N$.
Given:
Force $F = 5 \, N$
Acceleration $a_1 = 8 \, m s^{-2}$ for mass $m_1$
Acceleration $a_2 = 24 \, m s^{-2}$ for mass $m_2$
Calculating individual masses:
$m_1 = \frac{F}{a_1} = \frac{5}{8} \, kg$
$m_2 = \frac{F}{a_2} = \frac{5}{24} \, kg$
When both masses are tied together,the total mass $M$ is:
$M = m_1 + m_2 = \frac{5}{8} + \frac{5}{24} = \frac{15 + 5}{24} = \frac{20}{24} = \frac{5}{6} \, kg$
Acceleration $a$ produced by the same force $F$ on the combined mass $M$ is:
$a = \frac{F}{M} = \frac{5}{5/6} = 6 \, m s^{-2}$

(N/A) Momentum is defined as the product of the mass and velocity of an object. It is a vector quantity.
Momentum $(p)$ = mass $(m)$ $\times$ velocity $(v)$
The $SI$ unit of momentum is $kg\, m\, s^{-1}$.
Force is defined as the rate of change of momentum. According to Newton's second law of motion,the force applied on an object is directly proportional to the rate of change of its momentum.
Force $(F)$ = $\frac{\Delta p}{\Delta t}$
Graphical representation:
$(a)$ Since $p = mv$,if mass $(m)$ is fixed,momentum $(p)$ is directly proportional to velocity $(v)$. The graph of momentum versus velocity is a straight line passing through the origin.
$(b)$ Since $p = mv$,if velocity $(v)$ is constant,momentum $(p)$ is directly proportional to mass $(m)$. The graph of momentum versus mass is a straight line passing through the origin.

(B) Friction is a resistive force that acts only when there is relative motion or a tendency for relative motion between two surfaces in contact.
If a ball is at rest on a horizontal surface and no external force is applied to it,there is no tendency for the ball to move.
Therefore,the net force acting on the ball is zero,and the frictional force remains zero.
Friction does not initiate motion on its own; it only opposes the motion caused by an external force.

(B) According to Newton's second law of motion,the force $(F)$ is given by the product of mass $(m)$ and acceleration $(a)$.
Formula: $F = m \times a$
Given:
Mass $(m)$ = $2 \, kg$
Acceleration $(a)$ = $5 \, m s^{-2}$
Calculation:
$F = 2 \, kg \times 5 \, m s^{-2} = 10 \, N$
Therefore,the force required is $10 \, N$.

(A) According to Newton's $3^{rd}$ Law of Motion,every action has an equal and opposite reaction.
In this scenario,when the man jumps forward,he exerts a backward force on the boat,which is the action.
The boat simultaneously exerts an equal and opposite forward force on the man,which is the reaction.
Therefore,the push of the man on the boat is the action,and the force exerted by the boat on the man is the reaction.

(A) Inertia is the property of an object to resist a change in its state of motion or rest,and it is directly proportional to the mass of the object.
Since a basketball has a greater mass than a football,it possesses more inertia.
Therefore,a greater amount of force is required to overcome the inertia of the basketball compared to the football.

(N/A) The dust particles lying on the carpet possess inertia of rest. When the carpet is beaten with a stick,the carpet moves suddenly,but the dust particles tend to remain in their state of rest due to inertia of rest. Consequently,the dust particles get separated from the carpet and fall down due to gravity.

(B) When the brakes are applied,the car slows down,but due to the law of inertia,the body of the passenger continues to be in the same state of motion.
Safety belts exert a force on the body to slow down its forward motion,thereby preventing the passenger from hitting the dashboard or windshield.

(N/A) The physical quantity that measures the inertia of an object is its mass.
Inertia is the inherent property of a body to resist any change in its state of rest or uniform motion.
Greater the mass of an object,greater is its inertia.
The $SI$ unit of mass is kilogram $(kg).$

(A) The $SI$ unit of force is the Newton $(N)$,which is equivalent to $kg\, m s^{-2}$ according to Newton's second law $(F = ma)$.
The $SI$ unit of momentum $(p)$ is the product of mass and velocity $(p = mv)$,which is $kg\, m s^{-1}$.
Therefore,the units for force and momentum are $kg\, m s^{-2}$ and $kg\, m s^{-1}$ respectively.

(A) According to Newton's First Law of Motion,an object moving with a constant velocity in a straight line will continue to do so unless acted upon by an external unbalanced force.
Since the book is moving with a constant velocity of $4 \, m s^{-1}$ on a frictionless surface,its acceleration is zero $(a = 0)$.
Using Newton's Second Law,$F = m \times a$,where $m = 2 \, kg$ and $a = 0$.
Therefore,$F = 2 \, kg \times 0 \, m s^{-2} = 0 \, N$.
Thus,zero force is required to maintain the same velocity.

(N/A) Momentum $(p)$ is defined as the product of mass $(m)$ and velocity $(v)$.
The mathematical formula is: $p = m \times v$.
The $SI$ unit of mass is kilogram $(kg)$ and the $SI$ unit of velocity is metre per second $(m/s)$.
Therefore,the $SI$ unit of momentum is kilogram metre per second,denoted as $kg \cdot m/s$ or $kg \cdot m \cdot s^{-1}$.

(D) According to Newton's second law of motion,the force $(F)$ is the product of mass $(m)$ and acceleration $(a)$.
Formula: $F = m \times a$
Given:
Mass $(m) = 6 \, kg$
Acceleration $(a) = 4 \, m s^{-2}$
Calculation:
$F = 6 \, kg \times 4 \, m s^{-2} = 24 \, N$
Therefore,the force required is $24 \, N$.

(A) Momentum $(p)$ is defined as the product of mass $(m)$ and velocity $(v)$,expressed as $p = m \times v$.
At the highest point of its trajectory,the ball momentarily comes to rest before falling back down,meaning its velocity $(v)$ is $0 \ m/s$.
Therefore,the momentum at the highest point is $p = m \times 0 = 0$.

(N/A) $(i)$ Lifting a bucket; lifting a stone.
$(ii)$ Pushing open a door; pushing a luggage trolley.
$(iii)$ Pulling of a train by an engine; pulling of a cart by a horse.
$(iv)$ Stretching a rubber balloon before inflating; stretching a spring.
$(v)$ Compressing the air with a piston; a doctor compressing the plunger of a syringe while injecting.
$(vi)$ Friction resists motion; air resistance opposes the motion of falling bodies.
$(vii)$ $A$ magnet attracting a piece of iron; a stone falling towards the ground due to gravity.
$(viii)$ Squeezing out the toothpaste from a tube; squeezing wet clothes.

(N/A) Newton's first law of motion,also known as the law of inertia,states that an object will remain at rest or continue to move at a constant velocity in a straight line unless acted upon by an external unbalanced force.
This law implies that objects have a natural tendency to resist changes in their state of motion,a property known as inertia.
For example,a book lying on a table will remain there until someone pushes it,and a ball rolling on a frictionless surface would theoretically continue moving forever unless stopped by an external force.

(B) According to Newton's third law of motion,for every action,there is an equal and opposite reaction.
When you kick a stone,your foot exerts a force on the stone (action).
Simultaneously,the stone exerts an equal and opposite force on your foot (reaction).
This reaction force from the hard surface of the stone causes the pain in your foot.

(N/A) force acting towards the centre of a circular path,known as centripetal force,in which a body moves with constant speed,merely changes the direction of motion of the body without changing its speed.

(N/A) $(i)$ Force is an external push or pull that changes or tends to change the state of rest or uniform motion of a body in a straight line.
$(ii)$ Dyne is the absolute unit of force in the $CGS$ system. One dyne is defined as the force that produces an acceleration of $1 \ cm \ s^{-2}$ when acting on a body of mass $1 \ g$.
$(iii)$ Newton is the absolute unit of force in the $SI$ system. One newton is defined as the force that produces an acceleration of $1 \ m \ s^{-2}$ when acting on a body of mass $1 \ kg$.

(N/A) Newton's second law of motion states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.
Mathematically,$F = ma$,where $F$ is the force,$m$ is the mass,and $a$ is the acceleration.

(B) The $SI$ unit of force is the Newton $(N)$.
It is defined as the force required to accelerate a mass of $1 \ kg$ by $1 \ m/s^2$.

(N/A) The $CGS$ unit of force is the dyne.
$1 \text{ Newton (N)} = 10^5 \text{ dynes}$.
This relationship is derived from the fact that $1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2$,and since $1 \text{ kg} = 10^3 \text{ g}$ and $1 \text{ m} = 10^2 \text{ cm}$,we get $1 \text{ N} = 10^3 \text{ g} \times 10^2 \text{ cm/s}^2 = 10^5 \text{ g} \cdot \text{cm/s}^2$,which is equal to $10^5 \text{ dynes}$.

(N/A) Newton's first law of motion states that an object remains in a state of rest or of uniform motion in a straight line unless it is compelled to change that state by an applied external force.
This law is also known as the Law of Inertia,as it describes the tendency of objects to resist changes in their state of motion.

(B) An athlete runs before taking a jump to gain momentum.
According to Newton's first law of motion,an object in motion tends to stay in motion.
By running,the athlete's body acquires a state of inertia of motion.
This momentum helps the athlete to cover a longer distance during the jump.

(N/A) $1\, kg$ weight is defined as the gravitational force exerted by the Earth on an object with a mass of $1\, kg$.
It is calculated using the formula $F = m \times g$,where $m = 1\, kg$ and $g \approx 9.8\, m/s^2$.
Therefore,$1\, kg\, wt = 1\, kg \times 9.8\, m/s^2 = 9.8\, N$.

(C) Glass or chinaware items are fragile and prone to breaking upon impact.
When these items are packed with straw,the straw acts as a cushion.
According to Newton's Second Law of Motion,the force exerted is inversely proportional to the time taken for the change in momentum $(F = \Delta p / \Delta t)$.
By using straw,the time taken for the change in momentum is increased during any sudden jerk or collision.
As a result,the force exerted on the glass or chinaware is significantly reduced,preventing breakage.

(A) According to Newton's second law of motion,the force exerted is given by $F = \frac{dp}{dt}$,where $dp$ is the change in momentum and $dt$ is the time taken.
When an athlete falls on a cushioned bed,the bed compresses,which increases the time $(dt)$ taken for the athlete to come to rest.
Since the force $(F)$ is inversely proportional to the time $(dt)$,an increase in time results in a significant decrease in the impulsive force exerted on the athlete.
This prevents the athlete from getting injured.

(N/A) When a speeding bus stops suddenly,the luggage continues to move forward due to the inertia of motion. This happens because the luggage is in a state of motion along with the bus,and according to Newton's first law of motion,it tends to maintain its state of motion. Consequently,if the luggage is not tied,it is likely to fall off the bus due to its inertia.

(A) We know that the force $F$ is calculated using the formula $F = m \times a$,where $m$ is mass and $a$ is acceleration.
For the first case:
$F_1 = m_1 \times a_1 = 1\, kg \times 10\, m s^{-2} = 10\, N$
For the second case:
$F_2 = m_2 \times a_2 = 2\, kg \times 4\, m s^{-2} = 8\, N$
Comparing the two forces,we find that $10\, N > 8\, N$,which means $F_1 > F_2$.
Therefore,accelerating a $1\, kg$ mass at $10\, m s^{-2}$ requires a greater force.

(B) When we stop pedalling,the external force that was maintaining the motion is removed. The bicycle begins to slow down because of the frictional force acting between the tires and the road,as well as air resistance,which opposes the motion of the bicycle.

(N/A) The inertia of a body depends on its $mass$. $A$ body with a larger $mass$ possesses greater inertia, while a body with a smaller $mass$ possesses lesser inertia. Therefore, $mass$ is the quantitative measure of the inertia of a body.

$(FORCE)$ The physical quantity whose $SI$ unit is "newton" $(N)$ is force. Force is defined as a push or pull acting on an object, which can cause an object to accelerate, decelerate, or change its shape.