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Right choice is (B) kinetic ENERGY

For explanation: An object in motion possesses a velocity “V” at any instant of time.

This energy is termed “kinetic energy” and is given by;

Kinetic Energy = 1/2 x m x v^2

where;

m = Mass of the object in motion

Correct answer is (d) ENERGY can neither be created nor destroyed

To explain 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. This is ALSO one of the fundamental concepts of thermodynamics.

The correct choice is (a) 80 J

Best explanation: The work done on a body is OBTAINED by CALCULATING the dot product of the force and DISPLACEMENT vector. Since the displacement is in the direction of the applied force, the work done is positive and is equal to 80 J.

Correct OPTION is (a) 50 kJ

Explanation: The work done by the body is 50 kJ. Hence by the work-energy theorem, we can SAY that the TOTAL change in energy is equal to the total work done. THEREFORE, the total change in energy is 50 kJ. Since only the ‘amount’ has been asked, the sign, which DENOTES the direction of energy transfer, does not matter.

The CORRECT answer is (d) 10000/3 W

Easy EXPLANATION: Density of WATER = 1000 kg/m^3

Mass of water in 10m^3 = 1000 x 10

 = 10,000 kg

Volume of water filled in 1s = 10/(5×60)

 = 1/30 m^3

Mass filled in 1s = 1/30 x 1000

 = 100/3 kg

Power = 100/3 x 10 x 5; [g = 10m/s^2]

 = 5000/3 W

Since 50% of power is wasted, power of motor = 5000/3 x 2

 = 10000/3 W.

Right choice is (a) Elastic potential energy

To explain I would say: The potential energy stored in a SPRING is the CONSEQUENCE of its elastic PROPERTY and hence it is also TERMED “elastic potential energy”. It can be stored when the spring is extended or compressed.

Right option is (b) 0.04J

The explanation is: Rotational kinetic ENERGY is given by 0.5*I*Ω^2. I of a solid SPHERE is given by (2/5)*m*r². So, rotational kinetic energy is 0.5*0.4*(200/1000)*(20/100)^2*5^2 = 0.04J.

The correct option is (a) 100 kgs^-2

Best EXPLANATION: FORCE on a elongated/compressed spring is GIVEN by F = k*x where k is spring constant and x is elongation/compression. So, 200 = k*2 which gives k = 100 kgs^-2.

Correct OPTION is (c) 10J

Easy explanation: The maximum height ATTAINED by particle is given by u^2/(2*G). So total work done would be gain in POTENTIAL energy i.e. m*g*h = m*g*(u^2/(2*g))= (200/1000)*10*(10^2/20) = 10.

The correct option is (a) The measure of energy change

For explanation I would say: WORK done in any system is a measure of the energy change in the system with its SURROUNDINGS. Work done and energy change are in PRACTICE the same. When a force is applied on a body and it MOVES and does some work. The amount of work done denotes energy change of the system with its surroundings.

Correct OPTION is (b) False

The best explanation: Work energy THEOREM holds for both positive and NEGATIVE work DONE. If the work doneis positive then final kinetic energy increases by the amount of the work and if work done is negative then final kinetic energy decreases by the amount of work done.

The correct ANSWER is (c) position

Explanation: PE = m x g x h

The mass of the given object is CONSTANT.

The FIXED reference indicates constant acceleration due to gravity.

Hence, VARIATION in height (h) is nothing but a variation in position.

Hence, the potential energy of an object of constant mass and fixed reference is DETERMINED by its position.

The correct answer is (c) 38 J

The best explanation: Displacement (d) = r2 – r1

 = (3I – 5J + 4K) m

Work = Force . Displacement; [Dot product of vectors]

 = (5i – 3j +2k) .(3i – 5j + 4k)

 = 38 J.

Correct answer is (a) 8000 J

The BEST explanation: Since the distance and time TAKEN are given, we can find out the acceleration of the BODY by the second equation of motion which is 4 m/s^2. From the second law of motion, the force can be found. Force = 160 N. From the force and the displacement, the work can be found out. Work = 8000 J.

The correct answer is (b) The ability to CREATE work

The explanation: Energy is defined as the ability to create work. When a force is applied on a BODY to create displacement, work TAKES place. Work is quantified by the force applied by the displacement. Whereas the energy is the ability of the force to create work. In general, the TOTAL INPUT energy = total output energy + work.

The CORRECT option is (a) Lost

Easiest explanation: Coefficient of restitution or e can be UNDERSTOOD as the measure of how much KINETIC energy is REMAINING after the collision. As e becomes lesser and lesser, more kinetic energy is lost in the collision. This can be easily understood with by deriving the coefficient of restitution in a completely elastic collision.

Correct OPTION is (a) Exchange

The explanation: In this CASE also we need to conserve the MOMENTUM and WRITE the expression for e. After doing so we will find that the sum of the initial velocities is equal to the sum of the final velocities. Same goes for the difference (with slight alterations). This will result in the final velocity of one body being equal to the initial velocity of the other. Hence, the velocities will get exchanged.

Right answer is (b) False

The explanation: When a roller coaster is at the top of a steep hill, its POTENTIAL ENERGY is MAXIMUM. When it hurdles down the slope and comes to the bottom, the potential energy reduces greatly. However, kinetic energy increases. Thus, there is a CHANGE from potential energy to kinetic energy and hence no destruction of energy.

The CORRECT choice is (a) 0 < e < 1

The best I can explain: Partially ELASTIC collision occurs when the value of e is LESS than one and more than zero. In this CASE the collision is neither perfectly elastic nor perfectly INELASTIC. Hence, we call it partially elastic collision.

Correct answer is (b) Limiting friction

To elaborate: The value of limiting friction can be found by equating it to the PRODUCT of the STATIC frictional COEFFICIENT and normal REACTION force of the body.

Right choice is (C) F = 2

Easiest explanation: F = x, F = x^2 varies with x and y co-ordinate RESPECTIVELY. F = 2*t varies with time but F = 2 is ALWAYS CONSTANT.

Right choice is (a) Kinetic energy decreases by half

To explain I WOULD SAY: Momentum doesn’t CHANGE i.e. (2m)*(v/2). K.E decreases by half while P.E BECOMES TWICE the original value.

Right option is (a) 5600 J

To EXPLAIN I WOULD say: Escape velocity of EARTH from the surface (v) = 11.2 km/s

 = 11,200 m/s

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

 = (1/2) x 1 x 11,200

 = 5600 J.

The CORRECT answer is (a) 16000 J

To explain: The work done on a body is obtained by CALCULATING the DOT product of the force and displacement vector. From Newton’s second law, we get the acceleration EQUAL to 8 m/s^2. From the second equation of motion the displacement COVERED can be obtained which is equal to 400 m. On taking the dot product of the force and displacement, we get work done equaling to 16000 J.

Correct option is (a) the top of the STEEP climb

The BEST I can explain: The potential ENERGY is given by;

PE = m x g x h

where;

PE = Potential energy

m = Mass of the object

g = ACCELERATION due to gravity

h = Height of the object

Hence, the higher the object, the greater the potential energy.

The correct choice is (a) [ML^2T^-2]

To ELABORATE: Energy = FORCE x Displacement

Units of energy = KG x (m/s^2) x m

 = kg x m^2 x s^-2

Therefore;

Dimensions of energy = [ML^2T^-2].

Right ANSWER is (b) False

Easy EXPLANATION: PE = 1/2 x k x d^2; where d = Displacement

Equation of PARABOLA: y = 4x^2

By comparing the two EQUATIONS, we can conclude that the elastic potential energy varies parabolically with displacement and not linearly.

The correct choice is (B) SLIDING friction and rolling friction

For explanation I would say: Kinetic friction is of two types; sliding and rolling. Rolling friction is less than sliding friction. This is the REASON why rolling a BODY is always easier than sliding a body.

The correct choice is (b) 114J

The BEST explanation: The force on a spring stretched by x meters is given by F = K*x where k is the spring constant. So, 600 = k*(2/100). Now k = 3*10^4, and hence F = 30000*x. W = \(\int_{x1}^{x2}\)F * dx = \(\int_{0.18}^{0.2}\)30000 * x * dx = 114 J.

The CORRECT option is (b) 4:25

Easiest EXPLANATION: From newtons law;

v1 = u + gt1

v1 = 2g

v2 = u + gt2

v2 = 5g

KE1 : KE2 = v1^2 : v2^2

 = 4 : 25.

Right answer is (a) 5 m/s

The explanation: The kinetic energy of MAN (initial) = KE

 = KE’/2

The kinetic energy of man (FINAL) = 2 x KE’

The kinetic energy of boy = KE’

Mass of man = M

Mass of boy = m

 = M/2

v = Initial VELOCITY of man

v’ = Initial velocity of boy

(1/2) x M x v^2= (1/2) x m x v’^2

 = (1/2) x M/2 x v’^2

Therefore; v = v’/2^0.5

(1/2) x M x (v+5) ^2=2 x (1/2) x m x v’^2

 = 2 x (1/2) x M/2 x (2 x v^2)

(v+5) ^2 = 4 x v^2

v + 5 = 2 x v

v = 5m/s.

Right choice is (a) 10 N

Explanation: The amount of WORK done on a body is obtained by calculating the dot product of the FORCE and the displacement. Due to lack of information, we ASSUME that the force and the displacement are in the same direction. Since the total work done is given, we can find out the applied force by DIVIDING the total work done by the total displacement. By doing so we get force applied = 10 N.

The CORRECT choice is (a) 400 J, 400 J

To explain I would say: By work-ENERGY theorem, the TOTAL work done on a BODY is equal to the change in the total energy. K.E. = \(\Big(\frac{1}{2}\Big)\)mv^2. The acceleration of the body is 4/2 = 2 m/s^2. The final velocity after 10 s can be found out by the first equation of motion. The total change in the total energy is the total change in kinetic energy as the body is moving on plane ground and is equal to 400 J. Hence the work done is 400 J.

Right choice is (c) 3

To EXPLAIN: The initial momentum of the system = momentum of car + momentum of truck = 40 Kg-m/s leftwards. Since the momentum is conserved, the initial momentum = FINAL momentum. Hence the final momentum is 40 Kg-m/s leftwards. The collision is perfectly elastic, THEREFORE, e = 1. Therefore, final relative velocity (of truck with respect to car) = initial relative velocity (of truck with respect to car). Sum of the final velocities of the car and the truck = 4 m/s. From this information and the conservation of momentum, one can FIND the final velocity of the truck.

The correct choice is (c) Thrice as HIGH height as ball B

Explanation: PEa = (m x g x h) a

PEb = (m x g x h) b

ma = MB = m

GA = gb = g

PEa = 3 x PEb

ma x ga x ha = mb x gb x hb x 3

m x g x ha = m x g x hb x 3

ha = 3 x hb.

Correct OPTION is (a) 200 J

Easiest explanation: MASS DENSITY (p) = 0.4 kg/m

Length (l) = 10 m

Force = f(X)

 = m(x)*G

 = 0.4x*g

 = 4x

Displacement (d) = 10 m

Work = \(\int_{0}^{l}\)f(x)dx

 = \(\int_{0}^{10}\)4xdx

 = 200 J.

Correct answer is (a) There are multiple forces ACTION on the body

To explain I would say: The possible reason for this is that multiple forces are acting on the body at different instances throughout its MOTION. The work DONE on a body is a MEASURE of the energy exchanged between the body and the environment and is usually the total work done. Work done due to the given force is 20 J but this need not be the total work done.

Correct answer is (a) It MOVES slowly

For explanation: The total change in energy is CONSTITUTED by the changes in POTENTIAL and kinetic energies. When the body is moving slowly, it implies that the body is moving with such a small velocity that the square of the velocity in the expression of kinetic energy becomes negligible. Hence, the total change in the energy is constituted by the total change in the potential energy.