Sure, here are sample questions based on the topics of “Unit & Dimensions” and “Work, Power, and Energy” that could appear in a previous NEET exam:

1. Unit & Dimensions:

Question:

If the force \( F \), velocity \( v \), and time \( t \) are taken as fundamental quantities, what would be the dimensions of mass \( m \) in terms of \( F \), \( v \), and \( t \)?

**(A) \( [Fv^{-1}t] \)**

**(B) \( [Fvt^{-1}] \)**

**(C) \( [Fv^{-2}t^2] \)**

**(D) \( [Fv^{-1}t^{-1}] \)**

2. Work, Power, and Energy:

Question:

A force \( F = 5x \) acts on a particle in the x-direction, where \( F \) is in Newtons and \( x \) is in meters. How much work is done by this force as the particle moves from \( x = 0 \) to \( x = 2 \) meters?

(A) 5 J

(B) 10 J

(C) 20 J

(D) 25 J

3. Unit & Dimensions:

Question:

The velocity \( v \) of a particle is given by \( v = at + bt^2 \), where \( v \) is in meters per second and \( t \) is in seconds. What are the dimensions of the constants \( a \) and \( b \)?

(A) \( [L T^{-2}] \) and \( [L T^{-3}] \)

(B) \( [L T^{-1}] \) and \( [L T^{-2}] \)

(C) \( [L] \) and \( [T^{-2}] \)

(D) \( [L T^{-1}] \) and \( [L T^{-1}] \)

4. Work, Power, and Energy:

Question:

A 10 kg object is raised to a height of 5 meters. What is the potential energy stored in the object? (Take \( g = 9.8 \, m/s^2 \))

(A) 49 J

(B) 98 J

(C) 245 J

(D) 490 J

5. Unit & Dimensions:

Question:

The dimensions of Planck’s constant \( h \) are the same as that of

(A) Angular momentum

(B) Energy

(C) Force

**(D)** Power

6. Work, Power, and Energy:

**Question:**

A bullet of mass 10 g is fired with a velocity of 400 m/s. What is the kinetic energy of the bullet?

**(A)** 80 J

**(B)** 320 J

**(C)** 400 J

**(D)** 800 J

7. Unit & Dimensions:

Question:

Which of the following pairs of physical quantities have the same dimensions?

**(A)** Force and Power

**(B)** Work and Energy

**(C)** Torque and Angular Momentum

**(D)** Momentum and Energy

8. Work, Power, and Energy:

Question:

A machine does 500 J of work in 10 seconds. What is its power output?

**(A)** 50 W

**(B)** 100 W

**(C)** 500 W

**(D)** 1000 W

9. Unit & Dimensions:

Question:

If the energy \( E \) of a system depends on the permittivity \( \epsilon_0 \), electric field \( E \), and length \( L \), then the dimensional formula for energy is

**(A)** \( [\epsilon_0 E^2 L^3] \)

**(B)** \( [\epsilon_0 E^2 L^{-1}] \)

**(C)** \( [\epsilon_0^2 E^2 L^2] \)

**(D)** \( [\epsilon_0 E^2 L] \)

10. Work, Power, and Energy:

Question:

A spring with a spring constant \( k = 200 \, N/m \) is compressed by 0.1 meters. What is the potential energy stored in the spring?

**(A)** 1 J

**(B)** 2 J

**(C)** 0.5 J

**(D)** 0.2 J

11. Unit & Dimensions:

Question:

The dimensional formula of the universal gravitational constant \( G \) is

**(A)** \( [M^{-1} L^3 T^{-2}] \)

**(B)** \( [M^1 L^3 T^{-2}] \)

**(C)** \( [M^{-1} L^2 T^{-2}] \)

**(D)** \( [M^1 L^{-3} T^{-2}] \)

12. Work, Power, and Energy:

**Question:**

A force \( F = 10 \, N \) acts on a body at an angle of \( 60^\circ \) with the horizontal. The body moves horizontally by 5 meters. Calculate the work done by the force.

**(A)** 50 J

**(B)** 25 J

**(C)** 100 J

**(D)** 10 J

13. Unit & Dimensions:

**Question:**

Which one of the following physical quantities is dimensionless?

**(A)** Strain

**(B)** Stress

**(C)** Force

**(D)** Pressure

14. Work, Power, and Energy:

Question:

A car accelerates from rest to a velocity of \( 20 \, m/s \) in 10 seconds. If the mass of the car is 1000 kg, calculate the kinetic energy of the car at \( 20 \, m/s \).

**(A)** 200,000 J

**(B)** 100,000 J

**(C)** 50,000 J

**(D)** 400,000 J

15. Unit & Dimensions:

Question:

The dimensions of surface tension are

**(A)** \( [M T^{-2}] \)

**(B)** \( [M L^0 T^{-2}] \)

**(C)** \( [M L^2 T^{-2}] \)

**(D)** \( [M L T^{-2}] \)

16. Work, Power, and Energy:

**Question:**

Two bodies of masses \( m_1 \) and \( m_2 \) are moving with velocities \( v_1 \) and \( v_2 \) respectively. The ratio of their kinetic energies is

**(A)** \( \frac{m_1 v_1^2}{m_2 v_2^2} \)

**(B)** \( \frac{m_2 v_2^2}{m_1 v_1^2} \)

**(C)** \( \frac{m_1 v_2^2}{m_2 v_1^2} \)

**(D)** \( \frac{m_1^2 v_1}{m_2^2 v_2} \)

17. Unit & Dimensions:

**Question:**

Which of the following sets of quantities have the same dimensional formula?

**(A)** Pressure, Stress, Energy density

**(B)** Work, Power, Momentum

**(C)** Torque, Work, Angular Momentum

**(D)** Energy, Force, Power

18. Work, Power, and Energy:

**Question:**

A 60 W light bulb is used for 6 hours. How much energy does it consume in kilowatt-hours (kWh)?

**(A)** 0.36 kWh

**(B)** 3.6 kWh

**(C)** 21.6 kWh

**(D)** 0.216 kWh

19. Unit & Dimensions:

**Question:**

The dimensional formula for Planck’s constant \( h \) can be represented as

**(A)** \( [M L^2 T^{-1}] \)

**(B)** \( [M^2 L^2 T^{-2}] \)

**(C)** \( [M^1 L^2 T^{-2}] \)

**(D)** \( [M L^3 T^{-2}] \)

20. Work, Power, and Energy:

**Question:**

A body of mass 5 kg is moving at a speed of 10 m/s. What is the kinetic energy of the body?

**(A)** 250 J

**(B)** 500 J

**(C)** 50 J

**(D)** 100 J

21. Unit & Dimensions:

**Question:**

Which one of the following pairs has the same dimensional formula?

**(A)** Impulse and Momentum

**(B)** Force and Acceleration

**(C)** Work and Power

**(D)** Velocity and Energy

22. Work, Power, and Energy:

**Question:**

A crane lifts a mass of 200 kg to a height of 50 meters in 20 seconds. Calculate the power delivered by the crane. (Take \( g = 9.8 \, m/s^2 \))

**(A)** 500 W

**(B)** 980 W

**(C)** 4900 W

**(D)** 9800 W

23. Unit & Dimensions:

**Question:**

The dimensions of magnetic flux are

**(A)** \( [M T^{-1} I^{-1}] \)

**(B)** \( [M L^2 T^{-2} I^{-1}] \)

**(C)** \( [M L^2 T^{-2}] \)

**(D)** \( [M L T^{-1} I^{-1}] \)

24. Work, Power, and Energy:

**Question:**

An electric motor lifts a 100 kg object vertically upward with a constant velocity of 2 m/s. What is the power output of the motor? (Take \( g = 9.8 \, m/s^2 \))

**(A)** 196 W

**(B)** 980 W

**(C)** 1960 W

**(D)** 19600 W

25. Unit & Dimensions:

**Question:**

Which of the following quantities is dimensionless?

**(A)** Gravitational constant

**(B)** Refractive index

**(C)** Electric field

**(D)** Capacitance

26. Work, Power, and Energy:

Question:

The efficiency of a machine is 40%. If the machine consumes 1000 J of energy, how much useful work does it perform?

**(A)** 200 J

**(B)** 400 J

**(C)** 600 J

**(D)** 800 J

These questions are designed to test a range of knowledge in both dimensional analysis and the physics of work, power, and energy, helping to reinforce the concepts crucial for success in exams like NEET.

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