Let m1 and m2 be the masses of the bodies (m1>m2)

Initially, both are at rest. Hence their initial momenta are also zero.

We know, ∆P=final momentum -initial momentum

In this case, ∆P=final momentum=mv; where m= mass and v=velocity.

By definition of impulse, if the same interactive force act for the same time on bodies, the impulse is the same.

Hence ∆P is also the same which implies the final momentum is the same for both bodies.

From the definition of momentum, we can say greater mass will attain less speed. So it gains less acceleration. So, Options (a), (b) and (c) are incorrect.

Thus the body of greater mass will have the same momentum as the other body.

a rocket in space, the forces acting on the rocket include the thrust from the rocket engines and the gravitational force exerted by celestial bodies. The law of conservation of momentum can be used to predict the motion of the rocket based on the forces acting on it.

Use the following kinematic equation to calculate the velocity of the stone after 4 s.

v = u + gt

Since u = 0 m/s, it can be left out of the equation.

v = gt

v = -9.81 m/s² × 4 s = -39.24 m/s
Calculate the momentum=> p = mv
p = 2.5 kg × -39.24 m/s = -98.1 kg•m/s
The magnitude of momentum is 98.1 kg•m/s.

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal force back on the first object in the opposite direction. In the case of the stone, the reactive force would depend on the force applied to the stone and the weight of the stone. The greater the force applied or the heavier the stone, the greater the reactive force will be.

Use this equation:-

Vf = V0 + a * t
Vf = 0 + 9.8 m/s * 5 sec = 49 m/s

vf = Vi + gt

where vf is the velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time elapsed. Therefore, after falling for 5.0 s, the velocity of the ball would be: Also Vi=0

v = (9.8 m/s^2)(5.0 s) = 49 m/s

The correct answer is (b) Is constant but not zero.

According to Newton's second law of motion, the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. This means that if the mass is accelerating uniformly, the resultant force acting on it must be constant but not zero.

Option (a) is incorrect because if the force is zero, the mass will not accelerate. Option (c) is incorrect because the acceleration is uniform, not increasing uniformly with respect to time. Option (d) is incorrect because the acceleration is not necessarily related to the displacement of the mass from a fixed point.

Displacement Can never Be Greater than Distance but they both can equal in straight line path

The change in momentum of a body is equal to the impulse applied to that body. Impulse is a measure of the force applied to a body over a given period of time. It is equal to the force applied to the body multiplied by the time over which the force is applied.

In other words, the change in momentum of a body is given by the equation:

Δp = F*t

Let the length of tube be s.

Equation for uniformly accelerated motion: s = ut + ½ at²

The feather falls from rest. So, u = 0.

Time of fall, t = 0.5s (about 0.5s)

Acceleration a = acceleration of free fall = 9.81ms^-2

Length s = ut + ½ at² = 0 + ½ (9.81)(0.5)² = 1.226m

Since there is no extra force other than the action and reaction force so the linear momentum should be conserved.
Suppose the system moves with velocity  then momentum before collision is  and that after collision will be  (M + m)V

In a head-on elastic collision between two particles of equal mass where one is initially at rest, the moving particle comes to rest, and the stationary one takes up the velocity of the first. Hence, the velocity of the first particle after collision is zero.

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Newton's second law of motion establishes a relationship between force and acceleration.

According to Newton's second law, the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. This relationship can be expressed in the equation F = ma, where F is the force acting on the object, m is the mass of the object, and a is the acceleration of the object.

Quantity of Motion: This refers to momentum, which is the product of an object's mass and velocity (p = mv).

Momentum and Force: A moving object with momentum will exert a force on anything that tries to change its momentum (i.e., stop or change its direction). This is based on Newton's laws of motion.

Explanation of Incorrect MCQs

Inertia: Inertia is the tendency of an object to resist changes in its state of motion, but it doesn't directly describe the force exerted on another object.

Acceleration: Acceleration is the rate of change of velocity. While related to force and momentum, it's not the primary property responsible for exerting a force on an obstacle.

The weight of an object (W) is equal to its mass (m) multiplied by the acceleration due to gravity (g). This relationship can be expressed as the equation W = mg. Therefore, the ratio of weight to mass is equal to the acceleration due to gravity.

Bodies which fall freely under the action of gravity experience uniform acceleration.

Uniform acceleration refers to a constant rate of change of velocity over time. This means that the speed of an object with uniform acceleration is increasing at a constant rate. Falling under the influence of gravity is an example of uniform acceleration because the acceleration due to gravity (9.8 m/s²) is a constant, and the speed of an object falling freely increases at a constant rate as it falls.

Variable acceleration refers to a changing rate of change of velocity over time. This means that the speed of an object with variable acceleration is not increasing at a constant rate.

In this case, the car traveled a distance "d" on the way there and the same distance "d" on the way back, so it returned to its initial position and had a displacement of zero. Since the displacement is zero, the average velocity is also zero.

In an inelastic collision:

• Total momentum remains the same before and after the collision
• Total kinetic energy does not remain the same before and after collision
• Kinetic energy is lost due to dissipative factors like sound, friction, and heat
• Objects may deform or dent or even stick together

In an elastic collision:

• Total kinetic energy before and after the collision remains unchanged
• Total momentum before and after the collision remains unchanged
• Energy is not dissipated through heat or friction
• Colliding objects do not deform

By newton's 3rd law, the forces will be equal and opposite and change the momentum by equal and opposite (increase or decrease) amount. Hence 3rd law implies conservation of momentum.

the acceleration of the 1kg mass will be the total acceleration because in that case those 2 masses will act like one big mass.

Acceleration will be:

F=(m1+m2)a
=> a=F/(m1+m2)
=> a=40/(1+3)
=> a=10m/s^2

According to Newton's second law of motion, the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. This means that if the mass is accelerating uniformly, the resultant force acting on it must be constant but not zero.

(change in momentum)/time=force (weight)

$P=\sqrt{2m\mathrm{E)}}ifEareequalthenP\infty \sqrt{m}$

i.e. heavier body will possess greater momentum.

Note: Consider 19.6=20
and Consider 59.4=60

⇒ This can be put into words as follows: force equals the rate of change of momentum - this is a more general statement of Newton's second law of motion

⇒ The last equation may also be written in the form:

Where v² is the velocity after a force has been applied and V¹ is the velocity before the force has been applied

⇒ Impulse is the product of force and time and has the unit N s

Written Explanation

Since the momentum is the same, that means the quantity m1v1 = m2v2. This means that the mass and velocity change proportionally to each other so if you double m1 you would have to double m2 or v2 on the other side as well to maintain the same momentum. Now we consider the energy formula KE= ½ mv2 since the v is squared, it is the more important term to increase in order to make more energy. So if you double the mass of 1, then double the velocity of 2, you have the same momentum but the velocity of 2 when squared will make a greater energy, hence we want more velocity in object 2 to have more energy.