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Correct answer is (c) 1:9

To ELABORATE: PE1 = m x G x h

PE2 = (3M) x g x (3H)

 = 9 x m x g x h

PE1 : PE2 = mgh : 9mgh

 = 1:9.

Correct option is (c) It moves on an equipotential surface

Easiest EXPLANATION: An equipotential surface is defined as a surface on which the POTENTIAL of the body is same everywhere. Hence the potential of a body moving on an equipotential surface does not CHANGE. THEREFORE, the total change in energy is ATTRIBUTED by the change in the kinetic energy of the body.

Right choice is (a) Total WORK DONE

Best explanation: ACCORDING to the work-energy theorem, the total change in the energy of the system is equal to the total work done. LOSSES due to friction are also a part of the total work. The total work done is the sum of the work done by all the forces.

The correct answer is (b) POTENTIAL ENERGY

The best explanation: The potential energy of a body EMERGES due to its position. More specifically, the displacement of a body from the reference position decides the amount of potential energy it has. Usually, the potential energy of a body with mass m is given as P.E.=mgh, where h is the height of the body from the GROUND plane and g is the acceleration due to gravity. ABSOLUTE potential of a body cannot be found. Only the relative value can be found out.

Right option is (a) Impending MOTION

The best explanation: Impending motion is known as the motion that WOULD take place under the applied force if friction were absent. The motion which can’t proceed arbitrarily in any manner is called constrained motion. Motion without any restriction is known as an UNCONSTRAINED motion. ONE dimensional motion ALONG a straight line is known as linear motion.

The correct CHOICE is (a) NEWTONS

Easy explanation: The SI unit of FORCE is Newtons. While Joules, Ampere, and Mole are SI units of ENERGY, current and amount of SUBSTANCE.

Correct answer is (c) 75%

Best explanation: Initial KE = (1/2) x M x (60 x 60)

 = 1800 x M

From Newton’s laws;

s = UT + (1/2)gt^2

 = (60 x 3) – (10 x 3 x 3)/2

 = 180 – 45

 = 135 m

POTENTIAL ENERGY at 135m (PE) = M x g x s

 = 1350 x M

So KE at 135m = Initial KE – PE

 = 1800M – 1350M

 = 450M J; This is 25% of the initial kinetic energy. Hence, 75% is converted into potential energy.

The correct OPTION is (a) Mechanical WORK

Explanation: The work DONE by a force on a body is CALLED as mechanical work. In mechanical work, the mechanical energy of the body changes. Mechanical work = W = \(\vec{F}.\vec{s}\), where F is the force and s is the displacement.

Correct CHOICE is (a) Rate of doing WORK

To explain: Power is DEFINED as the rate of doing work. The ability to do work is energy. Energy can NEITHER be created nor be destroyed, hence, the rate of energy creation does not exist.

The correct answer is (B) 20 KW

Easy explanation: WEIGHT of car = m x g

 = 2,00 x 10

 = 2,000 N

Total force (F) = 2,000

Velocity (v) = 10 m/s

P = F x v

 = 2000 x 10

 = 20,000 W

 = 20 kW.

The correct ANSWER is (a) 25 kW

Easiest explanation: Weight of car = m x g

 = 200 x 10

 = 2,000 N

Frictional force = (25/100) x (2,000)

 = 500 N

Total force (F) = 2000 + 500

 = 2,500 N

Velocity (v) = 36 km/h

 = 36 x (1000/3600)

 = 10 m/s

P = F x v

 = 2500 x 10

 = 25 kW.

Correct OPTION is (b) 12m

To elaborate: PE of ball = m x g x h

 = 6 x 10 x 120

 = 7200 J

PE of spring = 1/2 x k x d^2

Given;

PE of ball = PE of spring

7200 = 1/2x k x d^2

 = 1/2 x 100 x d^2

d^2 = 144

d = 12 m.

Right option is (b) 225 W

Easy EXPLANATION: V = u + at

30 = a x 6

a = 5 m/s^2

Force (F) = m x a

 = 3 x 5

 = 15 N

v’ = u + at’

v’ = 5 x 3

 = 15 m/s

Power consumed in 3 seconds = F x v’

 = 15 X 15

 = 225 W.

The correct OPTION is (a) 1.96 m/s^2

Easiest EXPLANATION: Let the mass of the box be “m”

ma = u x mg

a = u x g

a = 0.2 x 9.81

 = 1.96 m/s^2.

Right OPTION is (b) 3K

The best explanation: K = 1/2 x m x V^2

New kinetic ENERGY (K’) = 1/2 x m’ x v’^2

m’ = 3m/4; [one-fourth of mass is REMOVED]

v’ = 2v; [velocity is DOUBLED]

K’ = 1/2 x (3m/4) x (2v) ^2

 = 1/2 x m x v x 3

 = 3 x K

 = 3K.

The CORRECT answer is (c) Nature of surfaces

For explanation I WOULD SAY: Since limiting friction depends only of the coefficient of friction of the surfaces, it, therefore, depends only of the nature of the SURFACE, i.e., smoothness or roughness.

Correct option is (B) 640 W

To elaborate: Since force is directly proportional to VELOCITY, the power REQUIRED will be directly proportional to the square of the velocity.

Power = Force x Velocity

Hence, power is a multiple of 8^2 and an INTEGER such that;

1000/10^2 = P/8^2

P = 640 W.

Right answer is (c) 25 J

For EXPLANATION I WOULD say: Maximum HEIGHT reached by the object;

h = v^2/(2 x G)

 = 25/20

 = 1.25 m

PE = m x g x h

 = 2 x 10 x 1.25

 = 25 J.

Right OPTION is (a) True

To elaborate: The POTENTIAL ENERGY can only be increased by external forces. Energy increase by internal forces manifests as an increase in kinetic energy. However, potential energy can be REDUCED by internal forces by increasing kinetic energy.

The correct ANSWER is (d) 2000 J

To EXPLAIN I would say: PE = m x G x h

m = 10 kg

g = 10 m/s^2

h = 20 m

PE = 10 x 10 x 20

 = 2000 J.

Right answer is (a) Amount of WORK done = 50 J

For explanation: By work-energy theorem, the total work done on a body is equal to the change in the total energy. No matter what kind of FORCE is ACTING on the SYSTEM, the theorem upholds. Since the total change in the energy is of 50 J, the total work done is equal to 50 J.