Unit & Dimensions ,work,power & Energy Test-NEET 2025

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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