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The correct choice is (b) Gets transferred

The best explanation: Energy INVOLVED in CREATING WORK gets transferred or converted into some other kind of energy. Energy can NEITHER be created nor be destroyed. HENCE, the energy involved will get converted into some other form of energy. Usually in mechanical work, the energy gets dissipated as heat energy.

Right answer is (d) 1100

The EXPLANATION: The initial momentum of the SYSTEM = momentum of ball + momentum of cube = 1100 Kg-m/s. Since the momentum is conserved, the initial momentum = FINAL momentum. Hence the final momentum is 1100 Kg-m/s.

Correct ANSWER is (b) 2 seconds

Best explanation: POWER (P) = Energy (E) X Time (t)

20,000 = (m x G x H) x t

 = (10 x 10 x 100) x t

t = 2 seconds.

Right OPTION is (a) True

Explanation: The area under this graph would be \(\int_{X1}^{x2}\)F * dx, which is WORK. Here x1 & x2 are two positions on the x-axis. Hence the statement is true.

The correct ANSWER is (a) 250

Explanation: Length (l) = 5 m

Height = DISPLACEMENT = 5 x sin30

 = 5 x (1/2)

 = 2.5

Force on object = m x G

= 10 X 10

 = 100 N

Work = Force x Displacement

 = 100 x 2.5

 = 250 Joules.

The CORRECT choice is (d) Inter-conversion of kinetic and potential energies

Easiest explanation: When a projectile MOVES, there is an inter-conversion of kinetic and potential energies. This is what CAUSES the body to cover a maximum vertical and horizontal distance. One might argue over the presence of gravity which is an external force. Well, the work done by gravity is NOTHING but the potential energy of the body which has already been taken care of in the expression for total energy.

Right CHOICE is (a) 200 J

The explanation is: Kinetic energy of a particle is GIVEN by 0.5*m*v^2 i.e. 0.5*1*20^2 = 200 J. Joules can also be written as kgm^-2s^-2.

Right answer is (a) P = dW/dt

Best explanation: Power is DEFINED as the rate of change of work. Hence, P = dW/dt. INSTANTANEOUS power = FORCE x instantaneous SPEED. Average power = total work / total TIME.

Correct option is (a) James Prescott Joule

Best explanation: The SI UNIT of energy is Joule. It has been named after the famous scientist James Prescott Joule. He made a SIGNIFICANT contribution to the WORD of SCIENCE by discovering the relationship of energy with MECHANICAL work.

Correct ANSWER is (c) 6

Easiest explanation: Power transmitted to machine = (90/100) x (1000) kW

 = 900 kW

Power USED to LIFT OBJECT = (80/100) x 900 KW

 = 720 kW

7,20,000 = F x v

 = (1/2 x m x v^2) x v

 = 10,000/2 x v^3

v^3 = 216

v = 6 m/s.

Right choice is (a) 7

To explain: The INITIAL momentum of the system = momentum of ball + momentum of cube = 1100 Kg-m/s eastwards. Since the momentum is CONSERVED, the initial momentum = final momentum. Hence the final momentum is 1100 Kg-m/s eastwards. The collision is perfectly ELASTIC, therefore, e = 1. Therefore, final relative VELOCITY (of cube with respect to ball) = initial relative velocity (of cube with respect to ball). Difference in the final velocities of cube and ball = 4 m/s. From this information and the CONSERVATION of momentum, one can find the final velocity of the cube.

Right option is (a) Momentum

The explanation is: Stress energy, CHEMICAL POTENTIAL and STRAIN energy are all energies and can be expressed in joules while momentum doesn’t FALL under energy category.

Correct choice is (b) Potential energy increases as ALTITUDE increases

The explanation: As altitude increases potential energy increases. From the equation of potential energy (PE);

PE = m x g x h

We can SEE that the potential energy is directly proportional to height. Hence the STATEMENT is justified.

Correct choice is (b) False

Best explanation: The FORMULA for KINETIC energy (KE) is as follows;

KE = (1/2) X m x v^2

v = VELOCITY of the object

From the formula, we can infer that the kinetic energy is INDEPENDENT of the acceleration of the object and only depends on the objects instantaneous velocity.

The correct answer is (a) 2000 J

To elaborate: The acceleration can be FOUND out by using the INITIAL and FINAL velocities and the time taken. Acceleration = 4 m/s^2. Force can be found out by the second law. By the second EQUATION of motion the distance covered in 5 s can be found which is equal to 50 m. Work can be found out by MULTIPLYING the force and the distance covered. Work = 2000 J.

Right answer is (a) SCALAR quantity

To EXPLAIN: Work DONE by a FORCE on a body is a scalar quantity. The work done is obtained by having a DOT product of the force vector with the displacement vector. The dot product of any two vectors gives a scalar as the result.

The correct answer is (d) 8

Easiest explanation: POWER = Force X Velocity

 = (Mass/Time) x Velocity^2

 = Rate of flow x Velocity^2

Rate of flow = Area x Velocity

Doubling the rate of flow will DOUBLE the velocity.

P = Rate of flow x Velocity^2

P’ = (2 x Rate of flow) x (2 x Velocity) ^2

 = 8P

P/P’ = 8.

Right CHOICE is (b) False

Easiest explanation: If a person consumes 3000 kcal of food and does a WORK requiring 2500 kcal of energy, the rest of the 500 kcal is mostly used for the metabolic activities of the body and some are lost in the FORM of HEAT energy to the atmosphere.

Right option is (d) Energy cannot be transformed

For EXPLANATION I WOULD say: According to the law of conservation of energy, energy can neither be created nor destroyed but can only be changed from one form to another. Energy in an open system can be VARYING because of constant matter and RADIATION exchanges with the SURROUNDING universe.

The correct ANSWER is (b) False

Explanation: A “variable force” is the force that CHANGES with time. This force can INCREASE or decrease at RANDOM time intervals. However, it is not constant with respect to time.

i.e., dF/dt is not EQUAL to “zero”.

Correct answer is (d) 10m

The EXPLANATION is: Let the VALUE of g = 10ms^-2. At the HIGHEST point, the KINETIC energy gets converted in to potential energy so, 200 [kgm^2s^-2] = 2*10*h [kgms^-2]. This gives h = 10m.

Correct OPTION is (a) Mechanical energy

Best explanation: Mechanical energy is COMPOSED of potential and kinetic energy. Potential energy is due to the position of the body. Kinetic energy is due to the motion of the body. Both when combined REPRESENT the total mechanical energy of the body.

Correct answer is (b) F^2/2k

For EXPLANATION I WOULD SAY: F = k*d

PE = 1/2*k*d^2

 = 1/2*F*d

 = 1/2*F*F/k

 = F^2/2k.

The correct choice is (a) The STATIONARY ball will start moving with a velocity V and the moving ball will come at rest

The EXPLANATION is: In this case also we NEED to conserve the momentum and write the expression for e. After some CALCULATION we will find that the stationary ball will start moving with a velocity v and the moving ball will come at rest.

Right option is (c) 31/3

Explanation: The initial momentum of the system = momentum of BALL + momentum of cube = 1100 Kg-m/s EASTWARDS. Since the momentum is conserved, the initial momentum = FINAL momentum. Hence the final momentum is 1100 Kg-m/s eastwards. The collision is perfectly elastic, THEREFORE, e = 1. Therefore, final relative velocity (of cube with respect to ball) = initial relative velocity (of cube with respect to ball). Sum of the final VELOCITIES of cube and ball = 10 m/s. From this information and the conservation of momentum, one can find the final velocity of the ball.

Right CHOICE is (c) Watt

To explain: The SI unit of power is “Watt”. It is named after the FAMOUS inventor “James Watt” who is widely remembered for his improvements on the steam engine.

1 Watt = 1 JOULE per second.

Correct option is (c) 13.5 J

The explanation: Work DONE is given by W = \(\int_{x1}^{X2}\)F * DX. So, W = \(\int_{2}^{5}\)(x + 1) * dx = [(5^2/2 + 5) – (2^2/2+2)] = 13.5.

The correct choice is (a) W = F * (X2 – X1)

The explanation is: Kinetic energy (K) = 1/2 x m x v^2

dK/dt = m*v*dv/dt

Force (F) = m*a

 = m*dv/dt

dK/dt = F*v

 = m*v*dv/dt

\(\int_{K1}^{K2}\) dK/dt = \(\int_{XA}^{Xb}\) F * dX/dt

\(\int_{K1}^{K2}\) dK = \(\int_{Xa}^{Xb}\) F * dX

K2 – K1 = F (X2 – X1)

W = F * (X2 – X1).

The CORRECT option is (a) True

Explanation: At the highest point of a PROJECTILE’s trajectory, the POTENTIAL energy is maximum because height is directly proportional to potential energy. The kinetic energy is minimum because velocity vectors has the least MAGNITUDE.

The correct option is (b) False

Easy explanation: When a body is falling freely under the influence of gravitythe kinetic ENERGY CHANGES as VELOCITY changes and the POTENTIAL energy changes because of change in height, However, because of the law of conservation of energy, the total mechanical energy remains constant.

Right answer is (b) Relative directions of FORCE and displacement

The EXPLANATION is: WORK is a scalar quantity; hence it cannot have a DIRECTION. But work is obtained by calculating the dot product of force and displacement. If both are in the same direction, the dot product is positive. If both are in opposite directions, the dot product is negative. Hence, the sign of work suggests the relative directions of force and displacement.

Correct OPTION is (a) Move together

To elaborate: In complete INELASTIC motion, the e VALUE is 0. Hence there is not relative motion between he TWO bodies. Therefore, the two bodies move together as a SINGLE body.

Right choice is (a) 980, gravity

The explanation: By work-energy theorem, the TOTAL work done on a BODY is EQUAL to the CHANGE in the total energy. Since the body is moving SLOWLY, the change in kinetic energy is negligible. P.E. = mgh. The change in potential energy and hence in the total energy is 980 J. Since only gravity is acting on the body, gravity is what causes the work.

Right option is (C) Total mechanical energy

Best explanation: For a body falling FREELY under the influence of gravity, the VELOCITY INCREASES as heigh decreases. Hence, there is a reduction in potential energy but an INCREASE in kinetic energy. However, the total mechanical energy, i.e., the sum of potential and kinetic energy always remains constant as per the law of conservation of energy.

The correct option is (a) 1

Explanation: A perfectly elastic collision occurs when the VALUE of e is 1. When the value of e is less than one the collision starts to becomes INELASTIC.

The CORRECT option is (b) 1000 J

The explanation is: PE = m x g x h

m = 5 kg

g = 10 m/s^2

Let;

H1 = 10m

h2 = 30m

PE1 = 5 x 10 x 10

 = 500 J

PE2 = 5 x 10 x 30

 = 1500 J

Increment in PE = PE2 – PE1

 = 1500 – 500

 = 1000 J.

Correct answer is (B) 40 J

The best I can EXPLAIN: MASS per length of chain (p) = 8/4 = 2 kg/m

Mass of ‘X’ m of length = 2x kg

Force = \(\int_{0}^{2}\)(2x * g)dx

 = \(\int_{0}^{2}\)20xdx

 = 40 J.

The correct ANSWER is (d) 0

For explanation I would say: A perfectly inelastic COLLISION OCCURS when the value of e is 0. When the value of e is more than 0 the collision STARTS to becomes ELASTIC.

Right CHOICE is (c) 900 W

Explanation: No. of bullets fired per second = 360/60 = 6

POWER of the gun is completely TRANSMITTED to bullets.

Power (P) = Power of bullets in 1 second

 = [(1/2 X m x v^2) x 6] / 1

m = 5 x 10^-3 kg

v = 600 m/s

P = (1/2 x 5 x 10^-3 x 600^2 x 6) / 1

 = 900 W.

The correct answer is (d) 10 m/s^2

Explanation: a = G (SIN θ – U COS θ)

a = 9.81 (sin(30) – 0.15 cos(30))

 = 9.81 x (0.5 – 0.13)

 = 3.63 m/s^2.

Right ANSWER is (b) False

The best I can explain: Friction is a self-adjusting force and depends on the normal REACTION which varies with the applied force. HOWEVER, the maximum magnitude of the force of friction is limited to the product of the coefficient of friction and weight of the object under static CONDITIONS.

The correct option is (d) 10000m J

For EXPLANATION I would say: Mass of object = m

From the conservation of energy;

1/2 x m x v^2 = m x G x h

 = m x 10 x 1000

 = 10000m J

The CORRECT option is (a) True

The explanation: Since the VALUE of static frictional force is GREATER than the kinetic frictional force, DIVIDING both values with constant normal reaction force yields a greater value of the static coefficient of friction.