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The answer is (C) will become doubled

Change in momentum = mu - (-mu) = 2 mu

The density of steel is more than that aluminium and wood. So, its mass is greater than the solids made of aluminium and wood. Inertia depends on the mass of the object. Hence, steel has a higher inertia.

Some of the methods to reduce friction are: 

(a) By polishing 

(b) By using ball bearings 

(c) By lubrication 

(d) By streamlining

The answer is (A) F = ma

When an object is moving with constant velocity then change in acceleration would be zero,

i.e., u = v = 40 m/s

\(a=\frac {\upsilon -u}{t} =\frac {40-40}{10} =\frac {0}{10} =0m/{s}^{2} \)

A major part of momentum goes to earth, and remaining part is transferred to molecules.

Advantages of friction:

(i) Friction helps us in walking on the floor.

(ii) We can not fix a nail in the wood or wall if there is no friction. It is friction which holds the nail.

(iii) A horse cannot pull a cart unless friction furnishes him a secure foothold.

(iv) Friction helps in applying brakes to stop a vehicle.

(v) Without friction, we cannot write on a paper or on a board.

Disadvantages of friction:

(i) It opposes the motion.

(ii) Due to friction, noise is produced in machines.

(iii) Due to friction, there is a loss of energy, which decreases the efficiency of an engine.

(iv) Due to friction, engines of automobiles consumes approximately 20% excess fuel which is a money loser.

(v) Due to friction, we have to exert more power in machines.

The momentum of a body is equal to the vector product of mass (m) and the velocity (v) of the body. In magnitude form, p = m x v and its S.I. the unit is kg m/s.

The truck and a car have the same momentum. 

i.e., p₁ = MV where M is mass of truck and V velocity of the truck 

Similarly, p₂ = mv where m is mass of the car, v is the velocity of the car Obviously mass of truck is greater than the mass of the car, so the speed of car will be more than truck in order to make p₁ = p₂

It gives the displacement of the object in the given time interval.

For a uniformly accelerated van, average velocity is given by

\(\frac{u+v}{2}\) = \(\frac{5+25}{2}\) = 15 m/s

(1) OA represents uniform acceleration since the slope of OA in the velocity-time graph is having a uniform positive slope. AB represents the uniform velocity of 20 ms^-1. Since the slope of AB is zero hence, acceleration is zero.

(2) After 10s, the velocity is 20 ms^-1 up to 30s and after 30 s, the velocity is uniformly restarted to zero after 40 s.

(3) Retardation is uniform and it is equal to the slope of BC, i.e.

slope of BC = \(\frac{BD}{DC}=\frac{20}{40-30}\) = 2ms^-2

And acceleration = -2 ms^-2

(4) Distance covered by the body between the 10th and 30th second

= 20 x 20 = 400 metres

The initial velocity of the truck (u) = 0 (As the truck is initially at rest)

Distance covered (s) = 400 m,

Time (t) = 20 sec

Mass of the truck (m)

= 7 metric tonnes = 7 x 1000

= 7000 kg

To find: Acceleration (a) = ?

Force (F) = ?

Using second equation of motion

S = ut + \(\frac{1}{2}\) at

400 = 0 x 20 + \(\frac{1}{2}\) x a x (20)²

⇒ 400 = \(\frac{1}{2}\) x a x 400

⇒ a = 2m/s² 

Now F = ma = 7000 x 2

= 14000 kgm/s² = 14000 Newton

The answer is (A) 47 m/sec

The answer is (A) 21 m/sec

(1) Uniformly accelerated motion, since the slope of the velocity-time graph is positive and uniform.

(2) It represents acceleration.

(3) The area below the velocity-time graph and time axis represents the distance covered.

(4) The area covered in 15 s i.e., area of triangle OBC gives the distance covered in 15 s.

∴ Distance covered

= \(\frac{1}{2}\) x BC x OC 

= \(\frac{1}{2}\) x 30 x 15 Distance 

= 225 m.

We are given that

Case - I:

when t = 0, u = 0 when t = 8 sec, v = ?

Acceleration (a) = 5 m/s²

∴ v = u + at

= 0 + 5 x 8 = 40 m/s

s = ut + \(\frac{1}{2}\) at²

s = 0 + \(\frac{1}{2}\) x 5 x (8)² = \(\frac{1}{2}\) x 5 x 64 = 160m

Case-II: t = 8 sec to t = 12 sec.

Distance = speed x time

= 40 x 4 = 160 m.

So, the total distance travelled

= 160 + 160 = 320 m.

Again, in this motion the initial and final positions are same 

So, displacement t = final position – initial position = 0 

Here, radius of circle = 2r So, circumference = 2n x 2r = 4πr 

Now, since the body completes 2 rounds, so total distance travelled = 2 x circumference = 2 x 47πr = 8πr .

A force is that cause which changes or tends to change the state of rest or of uniform motion of a body. Force is a vector quantity. 

The potential energy of a body is the energy possessed by body by virture of its state or position.

Given, Mass = 0.2kg

Height, h = 10m to 6m

Loss in potential energy = mg(h₁ - h₂)

= 0.2 x 10(10 - 6) = 8J

Work is said to be done when a force displaces a body through some distance, in its own direction, 

i.e., Work = Force × Displacement 

W = F × d 

Work is a scalar quantity.

Force due to gravity on the body F = mg 

Work done in lifting the body against the force of gravity to a height h above the ground 

W = F × d = mg × h = mgh 

Thus, potential energy of body = mgh.

Energy is defined as the capacity of a body to do work. Energy is a scalar quantity. The energy possessed by a body is measured by the amount of work done by a body while changing its state of rest or state of motion.

The man moving along the slope expends more energy. It is because, while moving along slope, he gains height and hence has extra potential energy.

 1KWh = 1KW × 1 h = 1000W × 3600s = 36,00,000J.

The kinetic energy possessed by a moving body is measured by the amount of work done by an opposing force in bringing the body to rest from its present state of motion.

At each of circular path, the particle, instead of moving straight continuously, turns towards the centre. Therefore, the motion in circular path is under the action of a force which called the centripetal force.

(a) They act in opposite directions.

(b) No, centrifugal force is not the force of reaction of centripetal force.

Both centripetal force and centrifugal force have same magnitude but they are opposite in direction. 

The man moving along the slope expends more energy. It is because, while moving along slope, he gains height and hence has extra potential energy.

(i) P.E. 

(ii) P.E. 

(iii) K.E. 

(iv) K.E. 

(v) P.E. 

(vi) K.E. 

(vii) K.E. 

(viii) P.E.

The momentum of a body is the product of the mass of the body and its velocity, i.e. p = mv. 

Moment of couple = F x Arm of couple

21Nm = F x 63cm

21Nm = F x 0.63m

F = 21/0.63 = 33.33N.

Moment of force depends on two factors: 

(i) Magnitude of force applied. 

(ii) Distance of line of action of the force from the axis of rotation.

Direction of centripetal force is towards the centre of the circle whereas centrifugal force is opposite to centripetal force. 

Force is equal to the rate of change of momentum.

Moment of couple = Force x Arm of couple

= 15 x 85N-cm.

= 15 x 85 x (1/100)Nm.

= 15 x 0.85

= 12.75Nm.

If mass of the body m remains constant then the change in momentum of the body depends only on the change in its velocity. 

 (i) Work done by a force is positive when the displacement is in the direction of the force. 

(ii) Work done by a force is negative when the displacement is in the direction opposite to the force.

Force required for uniform circular motion is centripetal force. It is directed towards its centre i.e., centre of the circle. 

A force is applied on 

(i) a non-rigid body and 

(ii) a rigid body. How does the effect of the force differ in the above two cases?

 Two effects of a force on a non-rigid body are: 

(i) Force can change the state of rest or motion of the body 

(ii) Force can change the size or shape of the body.

(i) Gain in speed: When number of teeth in driving wheel is more than number of teeth in driven wheel. 

(ii) Gain in torque: When number of teeth in driven gear is more than number of teeth in driving gear.

1. The kinetic energy of water molecules is released in the form of heat energy. 

2. The light energy changes to chemical energy? 

3. The chemical energy changes into heat energy. 

4. The electrical energy changes to chemical energy. 

5. The chemical energy changes into heat energy. 

6. The chemical energy changes into mechanical energy. 

7. The electrical energy changes into heat energy and light energy. 

8. The heat energy changes into electricity. 

9. The heat energy changes into electricity. 

10. The K. E. changes into electricity. 

11. The Kinetic energy changes into electricity.

A force can produce following three effects: 

(i) It can bring changes in dimensions. For example, in stretching a spring its length increases. 

(ii) It can start or stop motion. For example, a ball moves when kicked. 

(iii) It can changes speed or direction of motion. For example, a hockey player changes the speed and direction of motion of the ball by his stick.

The forces which act on a body without the help of any connector, are called non-contact forces or forces of distance. Gravitational force, Mechanical force etc., are non-contact forces. 

Net force acting on a body is equal to mass into acceleration or we may define force as a push or pull which changes or tends to change the state of rest or of uniform motion in a straight line of the body on which it acts. 

The forces acting on a man in a lift are 

(i) weight of the man acting vertically downwards, 

(ii) the reaction of the floor acting vertically upwards. 

In a lift accelerating downwards the net force on the man is 

F = m(g – a) = 50(9.8 – 2) 

= 50 × 7.8 = 390N. 

1. In the automobile engine, heat energy changes to kinetic energy. 

2. When two stones are rubbed against each other, kinetic energy changes to heat energy. 

3. When we speak in front of microphone, sound energy changes to electric energy. 

4. When a loudspeaker works, the electric energy changes to sound energy. 

5. During photosynthesis, light energy changes to chemical energy. 

6. During burning of magnesium, chemical energy changes to light energy. 

7. In an electric motor, electric energy changes to mechanical energy. 

8. In an electric generator, the mechanical energy changes to electric energy. 

9. The P.E. of stored water in dams, changes to electric energy in generators. 

10. When electrolysis is carried out, the electric energy changes to potential energy. 

11. Rubbing of palms. 

12. Throwing up a pebble from the ground. 

13. Electric heater while in use. 

14. Drawing current from an electric cell.