Explore topic-wise InterviewSolutions in .

(c) momentum

Correct answer is (d) Nm

Yes, if the external forces acting on the body can be represented in magnitude and direction by the sides of a closed polygon taken in the same order.

Given,

r = 10 cm = 0.1 m

radius at which it steps,

Centrifugal force = Remaining static friction

⇒ μ_smg = mrω²

ω = 90rpm

= \(\frac{90\times 2\pi}{60}\) rad/s

= 1.5 x 2π

= 3π rad/s

⇒ μ_s x m x 9.8  = m x 0.1 x 9π²

⇒ μ_s =  \(\frac{0.1\times 9 \times 9.8}{9.8}\)

= 0.9

Force of friction between the type and road provides centripetal force.

Correct answer is (c) mass

The amount of force required for a body of mass 1 gram produces an acceleration of 1 cm s^-2 ,1 dyne = 1 g cm s^-2 ; also 1N = 10⁵ dyne.

1N = 1 kg × 1 ms^-2

= (1000 g)(1000 cms^-2)

= 10⁵ gcm s^-2

i.e., 1 newton = 10⁵ dyne.

1 newton = 105 dyne

Correct answer is (c) Kg ms^-1

(c) momentum

Yes, if the external forces acting on the body can be represented in magnitude and direction by the sides of a closed polygon taken in the same order

(b) Conservation of momentum

Correct answer is (a) scooter

The force acting on an object is equal to the rate of change of its momentum –

\(\bar F\) = \(\frac{d\bar p}{dt}\)

correct answer is (b) 10^-5 N

(b) Newton’s second law

(b) Newton’s law of gravitation

(c) change of momentum

Correct answer is (c) Force

C) large force acts on the egg for shorter time.

(d) Both Assertion and Reason are true.

B) P – y, Q – z, R – x

A. (iv) 

B. (i)

C. (iii) 

D. (v) 

E. (ii)

(d) all the above

Correct answer is (b) \(\overrightarrow {F_{12}}\) = -\(\overrightarrow {F_{21}}\)

Correct anwer is (a) F₁₂ = F₂₁

Newton’s third law states that for every action there is an equal and opposite reaction.

Momentum and Newton’s Second Law of Motion Linear momentum : Momentum of body is the physical quantity of motion possessed by the body and mathematically. It is defined as the product of mass and velocity of the body.

As the linear momentum or simply momentum is equal to a scalar times a vector (velocity), it is therefore a vector quantity and is denoted by \(\vec{p}\). 

The momentum of a body of mass m moving with velocity \(\vec{v}\) is given by the relation :
\(\vec{p}=m \vec{v}\)
Dimensional formula = [M¹L¹T^-1]
Unit = Kg m/s
Suppose that a ball of mass m₁ and a car of mass m₂ (m₂ > m₁) are moving with the same velocity v. If P₁ and p₂ are momentum of ball and car respectively then :
\(\frac{p_{1}}{p_{2}}=\frac{m_{1} v}{m_{2} v}\) or \(\frac{p_{1}}{p_{2}}=\frac{m_{1}}{m_{2}}\)

As m₂ > m₁: It follows that p₂ > p₁. If a ball and a car are travelling with the same velocity, the momentum of the car will be greater than that of the ball. Similarly, we can show that if two objects of same masses are thrown at different velocities, the one moving with the greater velocity possesses greater momentum. Finally, if two objects of masses m₁ and m₂ are moving with velocities v₁ and v₂ possesses equal momentum.
m₁v₁ = m₂ v₂
\(\frac{v_{1}}{v_{2}}=\frac{m_{2}}{m_{1}}\)
In case m₂ > m₁ then v₂ < v₁ i. e, two bodies of different masses possess same momentum, the lighter body possesses greater velocity.

In case m₂ > m₁ then v₂ < v₁ i. e, two bodies of different masses possess same momentum, the lighter body possesses greater velocity.
The concept of momentum was introduced by Newton in order to measure the quantitative effect of force.
Momentum of body in term of kinetic energy
E_k = \(\frac{1}{2}\) mv² ……….. (1)
but p = mv
∴ v = p/m
put in equation (1)
E_k = \(\frac{1}{2} m \frac{p^{2}}{m^{2}}=\frac{p^{2}}{2 m}\)

(b) for a body in motion

Correct answer is (d) both a and c

Correct option is A) weight

A. (iv) 

B. (v) 

C. (ii) 

D. (i) 

E. (iii)

D) Both Pavithra and Teja are correct.

According to Newton’s first law of motion, in absence of external force, there is no change in state of a body and inertia is the property of a body due to which it opposes the change in its state. That is the reason. Newton’s first law of motion is also known as the law of inertia.

Correct answer is (d) both inertia and force

Everybody continues to be in its state of rest or uniform motion along a straight line unless compelled to change that state by an external force.

Correct option is A) 44. 64 N

Forces of action and reaction always act on different bodies, hence they never cancel each other.

B) action, reaction pair

Correct option is B) 8N

The correct option is (B) 8N,  This is because of Newton's 3rd law of motion

Proof. When we can show that Newton’s first and third law are contained in the second law, then we can say that it is the real law of motion.

(i) First law is contained in second law : According to Newton’s second law of motion \(\vec{F}=m\,\vec{a}\)

Where, m = mass of the body on which an external force \(\vec{F}\) is applied and acceleration \(\vec{a}\) is produced in it.

When no external force is applied on the body,

i. e.,

When \(\vec{F}\) = \(\vec{0}\), then from equation (1), we get \(m\,\vec{a}\) = \(\vec{0}\), but as m ≠ 0.

∴ \(\vec{a}\) = \(\vec{0}\)

It means that there will be no acceleration in the body if no external force is applied. This represents that a body at rest will remain at rest and a body is uniform motion will continue to move along the same straight line in the absence of an external force. This corresponds to Newton’s first law of motion. So, first law of motion is contained in Second law of motion.

(ii) Third law is contained in second law : Consider an isolates system of two bodies A and B. Let the act and react internally.

Suppose

F_AB = force applied on body A by body B.

And F_BA = force applied on body B by body A.

When, \(\frac {d\vec{p}_A}{dt}\) = rate of change of momentum of body A.

and \(\frac {d\vec{p}_B}{dt}\) = rate of change of momentum of body B.

Then, from Newton’s second law of motion.

F_AB = \(\frac {d\vec{p}_A}{dt}\)

F_BA = \(\frac {d\vec{p}_B}{dt}\)

Equation (2) and (3) gives

F_AB + F_BA = \(\frac{d}{dt}(\vec{p}_A)+\frac{d}{dt}(\vec{p}_B)\)

\(\frac{d}{dt}(\vec{p}_A+\vec{p}_B)\)

Since no external force acts on the system (∵ It is isolated), therefore according to Newton’s second law of motion,

\(\frac{d}{dt}(\vec{p}_1+\vec{p}_2)=\vec{0}\)

or \(\vec{F}_{AB}+\vec{F}_{BA}=\vec{0}\)

or \(\vec{F}_{AB}=-\vec{F}_{BA}\)

Action = −Reaction

It means that action and reaction are equal and opposite. It is the statement of Newton’s third law of motion. Thus, 3^rd law is contained in the second law of motion.

As both first and third law are contained in Second law, so Second law is the real law of motion.

According to Newton’s first law of motion, a body can’t change its state of rest or of uniform motion along a straight line unless an external force acts on it. It means that the natural tendency of the material body is now continue in the state of rest or that of uniform motion which is termed as inertia. Thus Newton’s first law is the law of inertia.

Correct option is D) None

The correct option is (D) None

Statement: The rate of change of linear momentum of a rigid body is directly proportional to the applied (external unbalanced) force and takes place in the direction of force.

\(\overset\rightarrow{F}=\frac{d\overset\rightarrow{p}}{dt}\)

Where, \(\overset\rightarrow{F}\) = Force applied

p = m \(\overset\rightarrow{v}\) = linear momentum

Importance of Newton’s second law:

1. It gives mathematical formulation for quantitative measure of force as rate of change of linear momentum.

2. It defines momentum instead of velocity as the fundamental quantity related to motion.

3. It takes into consideration the resultant unbalanced force on a body which is used to overcome Aristotle’s fallacy.

Correct answer is: Newton’s 2nd law

• Action and reaction are terms that express force. 
• These forces act in pairs. One force cannot exist by itself. 
• Action and reaction forces act simultaneously. 
• Action and reaction forces act on different objects. They do not act on the same object and hence cannot cancel each other’s effect.

Correct answer is: Newton’s 3rd law

‘Every action force has an equal and opposite reaction force which acts simultaneously’.

• Action and reaction are terms that express force. 
• These forces act in pairs. One force cannot exist by itself. 
• Action and reaction forces act simultaneously. 
• Action and reaction forces act on different objects. They do not act on the same object and hence cannot cancel each other’s effect.