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A variable force $F = (3x^2 + 2x)$ N acts on a particle, moving it along the x-axis from $x=1$ m to $x=3$ m. What is the change in kinetic energy of the particle during this displacement?

A

17 J

B

34 J

C

68 J

D

8.5 J

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Work Energy Theorem By Constant Force

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :2 mins

🔄Ncert Concepts :Work-Energy Theorem, Variable Force, Integration

A variable force $F = (6x) \hat{i}$ N acts on a particle of mass 2 kg, displacing it from $x = 0$ to $x = 3$ m. If the particle starts from rest, what is its final kinetic energy?

A

9 J

B

18 J

C

27 J

D

54 J

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Work Energy Theorem By Constant Force

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :3 mins

🔄Ncert Concepts :Work-Energy Theorem, Variable Force, Integration

A block of mass m is pushed up a rough inclined plane of angle $heta$ and coefficient of kinetic friction $\mu_k$ by a constant horizontal force F. The block moves a distance d along the incline. Which expression gives the net work done on the block?

A

Fd cos θ - mgd sin θ

B

Fd(cos θ - μk sin θ) - mgd(sin θ + μk cos θ)

C

Fd(cos θ + μk sin θ) - mgd sin θ

D

F cos θ - μk mg cos θ

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Work Energy Theorem By Constant Force

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :4 mins

🔄Ncert Concepts :Work-Energy Theorem, Constant Force, Friction, Inclined Plane

A particle moves along the x-axis under the influence of a force $F(x) = -kx + \frac{b}{x^3}$ , where k and b are positive constants. If the particle moves from $x = a$ to $x = 2a$ , where $a > 0$ , what is the work done by the force?

A

-3ka^2/2 + 3b/(8a^2)

B

-3ka^2/2 - 3b/(8a^2)

C

-ka^2 + b/(a^2)

D

-ka^2/2 + b/(8a^2)

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Work Energy Theorem By Constant Force

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :4 mins

🔄Ncert Concepts :Work-Energy Theorem, Variable Force, Integration

A block of mass 2 kg is sliding on a horizontal rough surface with an initial velocity of 5 m/s. If the coefficient of kinetic friction between the block and the surface is 0.2, how far will the block travel before coming to rest?

A

3.19 m

B

6.38 m

C

12.75 m

D

25.5 m

Question Tags

📚 Subject:Physics

📑 Chapter:Laws of Motion

🎯Topic:Motion On A Horizontal Rough Surface

🎓 Ncert Level:Application

🎯Difficulty :Medium

⚡ Time Required :2 mins

🔄Ncert Concepts :Work-Energy Theorem, Friction, Kinematics

Two identical balls of mass 'm' are moving with velocities 'v' and '2v' along the same line and undergo a perfectly inelastic collision. The fraction of the initial kinetic energy transformed into heat is:

A

1/10

B

1/5

C

1/2

D

9/10

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Inelastic Collision

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :3 mins

🔄Ncert Concepts :Inelastic Collision, Conservation of Momentum, Kinetic Energy

Two particles of masses 'm' and '2m' moving in opposite directions collide head-on elastically with velocities 'v' and 'v/2' respectively. The velocity of the particle of mass 'm' after the collision is:

A

v/2

B

-v

C

2v

D

-v/2

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Inelastic Collision

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :4 mins

🔄Ncert Concepts :Elastic Collision, Conservation of Momentum, Kinetic Energy

A particle of mass 'm' moving with velocity 'v' collides inelastically with another identical particle at rest. If the coefficient of restitution is 'e', the loss in kinetic energy of the system is:

A

$\frac{1}{2}mv^2(1-e^2)$

B

$\frac{1}{4}mv^2(1-e^2)$

C

$\frac{1}{2}mv^2(1-e)$

D

$\frac{1}{4}mv^2(1-e)$

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Inelastic Collision

🎓 Ncert Level:Application

🎯Difficulty :Hard

⚡ Time Required :4 mins

🔄Ncert Concepts :Inelastic Collision, Coefficient of Restitution, Conservation of Momentum, Kinetic Energy

A constant force of 10 N displaces an object by 5 m in the direction of the force. The work done is:

A

50 J

B

2 J

C

0.5 J

D

15 J

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Work Done By Constant Force

🎓 Ncert Level:Application

🎯Difficulty :Easy

⚡ Time Required :1 mins

🔄Ncert Concepts :Work, Energy, Power

A force of 20 N acts on a box, moving it 4 meters horizontally. If the force is applied at an angle of 30° to the horizontal, what is the work done?

A

80 J

B

69.3 J

C

40 J

D

10 J

Question Tags

📚 Subject:Physics

📑 Chapter:Work, Energy, and Power

🎯Topic:Work Done By Constant Force

🎓 Ncert Level:Application

🎯Difficulty :Easy

⚡ Time Required :1 mins

🔄Ncert Concepts :Work, Energy, Power

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