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No 

In an elastic collision, the total initial kinetic energy of the balls will be equal to the total final kinetic energy of the balls. This kinetic energy is not conserved at the instant the two balls are in contact with each other. In fact, at the time of collision, the kinetic energy of the balls will get converted into potential energy. 

Yes

In an elastic collision, the total linear momentum of the system always remains conserved

No; Yes

In an inelastic collision, there is always a loss of kinetic energy, i.e., the total kinetic energy of the billiard balls before collision will always be greater than that after collision

The total linear momentum of the system of billiards balls will remain conserved even in the case of an inelastic collision.

Elastic

In the given case, the forces involved are conservation. This is because they depend on the separation between the centres of the billiard balls. Hence, the collision is elastic. 

1. In this case total kinetic energy is not conserved because when the bodies are in contact during elastic collision even the kinetic energy is converted to potential energy. 

2. yes, because total momentum conserves as per the law of conservation of momentum. 

3. The answers are the same for an inelastic collision also. 

4. It is a case of elastic collision because in this case, the forces will be of conservative nature.

(d) becomes 4 times

Stone B with height h₂ has more energy, potential energy is present in it, when the stone falls on the sand it exerts more force than stone A due to more energy transformation. When the stone falls all the potential energy present in it, is transformed into kinetic energy.

One electron volt is equal to  6 x 10^-19J.

Correct answer is (d) 26 s

One horse power is equal to 746W.

Correct answer is (c) 100 J

(a) force and velocity.

p = 200 W t = 4s 

workdone = p x t 

200 x 4 = 800J

displecement = W/F = 800J/100N = 8m.

Power is measured in horse power. 1HP = 746W

Here, force = 20 N and displacement = 10 m 

Work = Force x Displacement 

= 20 N x 10 m = 200 Nm.

(a) Force F = W/s = 1000J/20m = 50N

(b) P = W/t = 1000J/4s = 250Js^-1 = 250W.

Formula → W = Fx s 

∴ W, work done → Joule 

= Newton x Metre; F,

 force → Newton; s, displacement → Metre

Uniform circular motion. 

1. When force is in the direction of displacement θ= 0°, then cos0 = 1. 

Hence, the work done by a force measured in the direction of displacement is W = F x S The work done is maximum and positive. 

2. When the displacement is in the direction making an angle . with the direction of force, Work done = Component of force in the direction of displacement x displacement 

W.F = cosθ x s .

(a) Force F = w/s = 1000J/20 = 50N

(b) P = w/t = 1000J/4s = 250JS^-1 = 250w

No of bullets, N = 10

Mass of each bullet, M = 20 × 10^-3kg

∴ Total mass of 10 bullets,

m = N × M

= 10 × 20 × 10^-3

= 200 × 10^-3kg

Velocity of each bullet = 300ms^-1

From, the equation, F = ma

=m\((\frac {v-u}{t})\)

= 200 × 10^-3 \((\frac {300-0}{1})\)

= 60 N

∴ Force required by the man to the gun to hold it in position is 60N.

If the number of bullets fired per sec doubles, then force required also doubles.

W = F x s 20 

= F x 2 

∴ F = 10 N

Mass of a body, m₁ = 50 kg

Mass of car m₂ = 200kg

velocity of the car v = 10ms^-1 g = 9.8ms^-2

P.E of the body, P.E = mgh

= 50 × 9.8 × h

= 490h

K.E of the car K.E = \(\frac{1}{2}\)m²v²

\(\frac{1}{2}\)× 200 × 10²

= 10,000J

But P.E of body = K.E of car

490h = 10,000

h = \(\frac{10,000}{490}\) = 20.41 m.

1. Energy = 6.4kJ = 6.4 x 1000J = 6400J 

S = 64m in the direction of force 

t = 2.5sec F = ? 

P = ? (in HP) 

Energy = Work done = F x S in the direction of force 

∴ F = Energy / S = 6400 / 64 = 100N 

Power = energy/Time = work/tTime = 6400/25 x 10 x 10 = 2560

2. W 

Power in Hp =2560/746=3.43 Hp

1. In photovoltaic cell, light energy is transformed into electrical energy. 

2. In an electromagnet, electrical energy is transformed into magnetic energy

m = 70kg, 

g = 10m/s²

h = 30m

Work W = mgh 

= 70 × 10 × 30 = 21000J

Time t = 5mt = 5 × 60 = 300s

Power p = \(\frac{w}{t}=\frac{21000}{300}\) = 70W

On pushing a pebble lying on a surface, it moves through a distance so work is done.

m = 50kg, 

g = 10m/s²

h = 15cm × 20 = 300cm = 8m

t = 60s

work W = mgh 

= 50 × 10 × 3 = 1500J

Power p = \(\frac{w}{t}=\frac{1500}{60}\) = 25W

F = 300N, s = 0 

w = Fs = 300 × 0 = 0

(a) Potential energy 

(b) Potential energy 

(c) Potential energy lesser. Kinetic energy greater

\(\because E_{k}=\frac{p^{2}}{2 m} \text { or } E_{k} \propto \frac{1}{m} \text { if } p\) is constant.

∵ The momentum of bullet and the gun is same, and the mass of bullet is less than that of the gun. Hence the kinetic energy of the bullet will be greater than that of the gun.

Kinetic energy: “Energy possessed by a body by virtue of its motion.” 

Examples : 

1. A bullet though of very small mass but moving with high speed and hence kinetic energy can peneterate a body. 

2. Running water of the river due its kinetic energy can rotate a turbine to produce electricity. 

3. A trunk running at high speed possesses kinetic energy and when hits a body can damage it. 

4. A shooting arrow possesses kinetic energy. 5. Blowing wind possesses K.E. 

Law of conservation of energy : “Energy can neither be created nor destroyed. Though it can be transformed from one form to other.”

The man who walk on a level road does no work as he is walking at right angle to the direction of gravitational force. Hence the man climbs a slope is doing more work.

(a) Potential energy, (stretched spring) 

(b) Kinetic energy as arrow is in motion 

(c) A stone lying on the top of a house has potential energy due to its position above the ground level. 

(d) Water stored in dam has potential energy.

(e) An electron spining around the nucleus has kinetic energy. 

(f) A fish moving in water has kinetic energy.