Lakhmir Singh & Manjit Kaur Test: Work & Energy - Class 9 MCQ

The Kinetic energy acquired by an object that is acted upon by a force is equal to the work done by the force. The work done by the force is equal to the force times the distance the object moved against the force. Therefore, in this case the Kinetic energy acquired by the body is equal to 25 N x 10 m = 250 J.
s=1/2at²
s=1/2x5x2x2
s=10

Topic in NCERT: WORK AND ENERGY

Line in NCERT: error Occcured while getting response from embedding

Object Falling from Rest. As an object falls from rest, its gravitational potential energy is converted to kinetic energy. Conservation of energy as a tool permits the calculation of the velocity just before it hits the surface. K.E. = J, which is of course equal to its initial potential energy.

Topic in NCERT: MECHANICAL ENERGY

Line in NCERT: "The sum of kinetic energy and potential energy of an object is its total mechanical energy. We find that during the free fall of the object, the decrease in potential energy, at any point in its path, appears as an equal amount of increase in kinetic energy."

The correct answer is B as Momentum = mass × velocity
4 = 25 × v
V = 4/25
V = 6.25

To find the kinetic energy ,
KE = 1/2 m v²
= 1/2 × 25 × 6.25 x 6.25
= 78.12 J
 

Topic in NCERT: KINETIC ENERGY

Line in NCERT: "Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = 1/2 mv²."

The correct answer is B as
 let the mass=m
then, m-3/4m=m/4
and velocity=2v
kinetic energy=1/2×mv²
=1/2×m/4×(2v²)
=1/2×m/4×4v²
=1/2mv²

Elastic Potential Energy:
Elastic potential energy is the energy stored in an elastic object when work is done upon it to compress or stretch it. It is a form of potential energy that is associated with the deformations of elastic materials.
Methods to Achieve Elastic Potential Energy:
The elastic potential energy of a body can be achieved by:
1. Compressing the Body:
- When a force is applied to compress a spring or any elastic object, work is done against the restoring force.
- The energy is stored in the object in the form of potential energy.
- For example, a compressed spring or a stretched rubber band.
2. Stretching the Body:
- When a force is applied to stretch an elastic object, work is done to overcome the elastic force.
- The energy is stored in the object as potential energy.
- For example, a stretched rubber band or a stretched balloon.
Incorrect Options:
A. Setting it into motion: This option does not directly result in the storage of elastic potential energy.
B. Raising the body to a height: This option refers to gravitational potential energy, not elastic potential energy.
C. Using an elastic band to tie the body: Tying a body with an elastic band does not directly result in the storage of elastic potential energy.
Conclusion:
To achieve elastic potential energy, the body needs to be compressed or stretched. This can be done by applying a force to the object, such as compressing a spring or stretching a rubber band. The potential energy is stored in the object due to the deformations caused by the applied force.

Topic in NCERT: POTENTIAL ENERGY

Line in NCERT: "The energy transferred to an object is stored as potential energy if it is not used to cause a change in the velocity or speed of the object. You transfer energy when you stretch a rubber band. The energy transferred to the band is its potential energy."

Kinetic Energy = (¹/₂) mv².

If the velocity of a body is halved, its kinetic energy becomes one fourth as kinetic energy is directly proportional to velocity squared.

Topic in NCERT: KINETIC ENERGY

Line in NCERT: "Ek = 1/2 mv²"

The potential energy (P.E.) at the height from which the fish dives is converted into kinetic energy (K.E.) as it hits the ground.

Given Data:

• Weight of the fish (W) = 35 kg
• Kinetic energy (K.E.) = 3500J
• Acceleration due to gravity (g) = 10m/s²

Formula:

Potential energy at height h:

P.E. = m⋅g⋅h

Since P.E.= K.E., we can equate:

m⋅g⋅h = 3500

Step 1: Solve for h

Substitute m=35 kg and g=10 m/s²:

35⋅10⋅h=3500

350⋅h = 3500

h=3500 / 350 =10 m

The correct option is D.
A moving car is an example of kinetic energy whereas water stored in a dam, compressed spring and stretched rubber band are examples of potential energy.

K.E = 0.5mv²
v = √(2K.E / m)
= √(2 × 625 Joule / 50 kg)
= √(625 Joule / 25 kg)
= 5 m/s...

Topic in NCERT: KINETIC ENERGY

Line in NCERT: "the kinetic energy possessed by an object of mass, m moving with a uniform velocity, v is Ek = 1/2 mv²"

Change in KE is workdone by work energy theoream 60-12 = 48J

since kinetic energies are equal

KE₁ = KE₂

mv₁²/2 = 4mv₂²/2

v₁/v₂ = √4/1 = 2:1

To determine the change in kinetic energy when the speed of an object doubles, we can refer to the equation for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
1. Initial kinetic energy: Let the initial speed of the object be "v" and its initial kinetic energy be "KEi".
2. Final kinetic energy: When the speed of the object doubles, its new speed becomes "2v". The final kinetic energy can be denoted as "KEf".
3. Comparing initial and final kinetic energies:
- Initial kinetic energy: KEi = 1/2 * mass * v^2
- Final kinetic energy: KEf = 1/2 * mass * (2v)^2 = 1/2 * mass * 4v^2
4. Simplifying the final kinetic energy expression:
KEf = 1/2 * mass * 4v^2 = 2 * (1/2 * mass * v^2) = 2 * KEi
Therefore, the final kinetic energy is double the initial kinetic energy when the speed of an object doubles. Hence, the correct answer is B: four times.

Topic in NCERT: KINETIC ENERGY

Line in NCERT: "Let us now express the kinetic energy of an object in the form of an equation. Consider an object of mass, m moving with a uniform velocity, u. The kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = 1/2 mv²."

KE = K = 1 /2( mv²) 
We know, p = mv
⇒ K = p² / 2m
 p²  =  2Km
As, KE is Same, ie . Constant, momentum would be directly proportional to the square root of mass.

One joule =1 newton x 1 meter

since one joule refers to the energy transferred to an object when a force of one newton acts on a body in the direction of motion through a distance of one meter.

Topic in NCERT: Energy

Line in NCERT: "1 J is the energy required to do 1 joule of work."

Mass (m)- 44 kg initial velocity (u) - 10m/s final velocity (v) - 0 time (t)- 10min =600s At first, acceleration (a) = v-u/t =0-10/600 = -1/60m per sec square using 2nd equation of motion s = ut +1/2at^2 s = 10*600 + 1/2*(-1/60*600*600) s=3000m Now, 2nd law of motion Force = ma = 44*(-1/60)=-11/15 N finally, work done=F*s=-11/15*3000= -22000J

Topic in NCERT: WORK AND ENERGY

Line in NCERT: "Consider a situation in which an object is moving with a uniform velocity along a particular direction. Now a retarding force, F, is applied in the opposite direction. That is, the angle between the two directions is 180°."

The correct option is D.
An object possesses gravitational potential energy if it is positioned at a height above (or below) the zero height. An object possesses elastic potential energy if it is at a position on an elastic medium other than the equilibrium position.

Topic in NCERT: POTENTIAL ENERGY OF AN OBJECT AT A HEIGHT

Line in NCERT: "An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy."

In physics the Kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. 

The correct option is Option C.
Potential energy is the energy that is stored in an object due to its position relative to some zero position. An object possesses gravitational potential energy if it is positioned at a height above (or below) the zero height.

Topic in NCERT: POTENTIAL ENERGY OF AN OBJECT AT A HEIGHT

Line in NCERT: "The potential energy possessed by the object is the energy present in it by virtue of its position or configuration."

The correct option is C.
 Both will have the same kinetic energy.