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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