1
Arjuna JEE (2026)
KPP - Formula Unit and Dimensions
S.N. Quantity Formula Unit Dimension
𝑑 Displacement or Distance
1. Velocity or speed (v) 𝑣= = m/s [𝑀0 𝐿1 𝑇 −1 ]
𝑡 Time
Δ𝑣 Change in velocity
2. Acceleration (a) 𝑎= = m/s 2 [𝑀0 𝐿𝑇 −2 ]
Δ𝑡 Change in time
3. Momentum (𝑃) 𝑃 = 𝑚𝑣 = Mass × Velocity kg − m/s [𝑀1 𝐿1 𝑇 −1 ]
Newton-
4. Impulse (I) 𝐼 = 𝐹 × Δ𝑡 = Force × Time second or kg − [𝑀1 𝐿1 𝑇 −1 ]
m/s
5. Force (F) 𝐹 = 𝑚𝑎 = Mass × Acceleration Newton [𝑀1 𝐿1 𝑇 −2 ]
𝐹 Force
6. Pressure (𝑃) 𝑃= = Pascal [𝑀1 𝐿−1 𝑇 −2 ]
𝐴 Area
1 1
7. Kinetic energy (𝐸𝐾 ) 𝐾 = 𝑚𝑣 2 = Mass × Velocity2 Joule [𝑀1 𝐿2 𝑇 −2 ]
2 2
𝑊 Work Watt or
8. Power (𝑃) 𝑃= = [𝑀1 𝐿2 𝑇 −3 ]
𝑡 Time Joule/sec
𝑚 Mass
9. Density (d) ρ= = kg/m3 [𝑀1 𝐿−3 𝑇 0 ]
𝑉 Volume
𝑆 Arc
10. Angular displacement (θ) θ= = Radian (rad.) [ 𝑀0 𝐿0 𝑇 0 ]
𝑟 Length
Δθ Angular displacement
11. Angular velocity (ω) ω= = Radian/sec [𝑀0 𝐿0 𝑇 −1 ]
Δ𝑡 Time
Δω Angular velocity
12. Angular acceleration (α) α= = Radian/sec2 [𝑀0 𝐿0 𝑇 −2 ]
Δ𝑡 Time
13. Moment of inertia (I) 𝐼 = 𝑚𝑥 2 = Mass × Distance2 kg − m2 [𝑀1 𝐿2 𝑇 0 ]
, 2
𝜏 = 𝐹 × 𝑟⊥ = Force × Perpendicular
14. Torque (𝜏) Newton-meter [𝑀1 𝐿2 𝑇 −2 ]
distance
15. Angular momentum (L) 𝐿 = 𝑚𝑣𝑟 = Mass × Velocity × Radius Joule-sec [𝑀1 𝐿2 𝑇 −1 ]
Force constant or spring 𝐹 = −𝑘𝑥 = Force constant ×
16. Newton/m [𝑀1 𝐿0 𝑇 −2 ]
constant (k) Displacement
𝐺𝑚1 𝑚2
𝐹=
𝑟2
17. Gravitational constant (𝐺) 𝑁 − 𝑚2 /𝑘 2 [𝑀−1 𝐿3 𝑇 −2 ]
Gravitational constant × Mass 2
=
Distance 2
𝑃𝑉 = 𝑛𝑅𝑇 Joule/mol-K [𝑀1 𝐿2 𝑇 −2 θ−1 ]
18. Gas constant (R) Pressure × Velocity = Gas constant ×
Temperature
𝐸 = h𝑣 Joule-s [𝑀1 𝐿2 𝑇 −1 ]
19. Planck's constant (h)
Energy = Planck's constant × Frequency
𝐹 Force N/m or
20. Surface tension (T) 𝑇= ⇒ Surface Tension = [𝑀1 𝐿0 𝑇 −2 ]
𝐼 Length joule/m2
𝐹 Force
21. Coefficient of viscosity () η= = kg/m − s [𝑀1 𝐿−1 𝑇 −1 ]
6π𝑟𝑣 Radius × Velocity
1 1
22. Time period (T) 𝑇= = Second [𝑀0 𝐿0 𝑇 1 ]
𝑛 Frequency
1 1
23. Frequency (𝑛) 𝑛= = Hz [𝑀0 𝐿0 𝑇 −1 ]
𝑇 Time
Dimensions of Quantities Related to Electricity and Heat:
S.N. Quantity Formula Unit Dimension
1. Heat (Q) Energy Joule [ML2 T −2 ]
Arjuna JEE (2026)
KPP - Formula Unit and Dimensions
S.N. Quantity Formula Unit Dimension
𝑑 Displacement or Distance
1. Velocity or speed (v) 𝑣= = m/s [𝑀0 𝐿1 𝑇 −1 ]
𝑡 Time
Δ𝑣 Change in velocity
2. Acceleration (a) 𝑎= = m/s 2 [𝑀0 𝐿𝑇 −2 ]
Δ𝑡 Change in time
3. Momentum (𝑃) 𝑃 = 𝑚𝑣 = Mass × Velocity kg − m/s [𝑀1 𝐿1 𝑇 −1 ]
Newton-
4. Impulse (I) 𝐼 = 𝐹 × Δ𝑡 = Force × Time second or kg − [𝑀1 𝐿1 𝑇 −1 ]
m/s
5. Force (F) 𝐹 = 𝑚𝑎 = Mass × Acceleration Newton [𝑀1 𝐿1 𝑇 −2 ]
𝐹 Force
6. Pressure (𝑃) 𝑃= = Pascal [𝑀1 𝐿−1 𝑇 −2 ]
𝐴 Area
1 1
7. Kinetic energy (𝐸𝐾 ) 𝐾 = 𝑚𝑣 2 = Mass × Velocity2 Joule [𝑀1 𝐿2 𝑇 −2 ]
2 2
𝑊 Work Watt or
8. Power (𝑃) 𝑃= = [𝑀1 𝐿2 𝑇 −3 ]
𝑡 Time Joule/sec
𝑚 Mass
9. Density (d) ρ= = kg/m3 [𝑀1 𝐿−3 𝑇 0 ]
𝑉 Volume
𝑆 Arc
10. Angular displacement (θ) θ= = Radian (rad.) [ 𝑀0 𝐿0 𝑇 0 ]
𝑟 Length
Δθ Angular displacement
11. Angular velocity (ω) ω= = Radian/sec [𝑀0 𝐿0 𝑇 −1 ]
Δ𝑡 Time
Δω Angular velocity
12. Angular acceleration (α) α= = Radian/sec2 [𝑀0 𝐿0 𝑇 −2 ]
Δ𝑡 Time
13. Moment of inertia (I) 𝐼 = 𝑚𝑥 2 = Mass × Distance2 kg − m2 [𝑀1 𝐿2 𝑇 0 ]
, 2
𝜏 = 𝐹 × 𝑟⊥ = Force × Perpendicular
14. Torque (𝜏) Newton-meter [𝑀1 𝐿2 𝑇 −2 ]
distance
15. Angular momentum (L) 𝐿 = 𝑚𝑣𝑟 = Mass × Velocity × Radius Joule-sec [𝑀1 𝐿2 𝑇 −1 ]
Force constant or spring 𝐹 = −𝑘𝑥 = Force constant ×
16. Newton/m [𝑀1 𝐿0 𝑇 −2 ]
constant (k) Displacement
𝐺𝑚1 𝑚2
𝐹=
𝑟2
17. Gravitational constant (𝐺) 𝑁 − 𝑚2 /𝑘 2 [𝑀−1 𝐿3 𝑇 −2 ]
Gravitational constant × Mass 2
=
Distance 2
𝑃𝑉 = 𝑛𝑅𝑇 Joule/mol-K [𝑀1 𝐿2 𝑇 −2 θ−1 ]
18. Gas constant (R) Pressure × Velocity = Gas constant ×
Temperature
𝐸 = h𝑣 Joule-s [𝑀1 𝐿2 𝑇 −1 ]
19. Planck's constant (h)
Energy = Planck's constant × Frequency
𝐹 Force N/m or
20. Surface tension (T) 𝑇= ⇒ Surface Tension = [𝑀1 𝐿0 𝑇 −2 ]
𝐼 Length joule/m2
𝐹 Force
21. Coefficient of viscosity () η= = kg/m − s [𝑀1 𝐿−1 𝑇 −1 ]
6π𝑟𝑣 Radius × Velocity
1 1
22. Time period (T) 𝑇= = Second [𝑀0 𝐿0 𝑇 1 ]
𝑛 Frequency
1 1
23. Frequency (𝑛) 𝑛= = Hz [𝑀0 𝐿0 𝑇 −1 ]
𝑇 Time
Dimensions of Quantities Related to Electricity and Heat:
S.N. Quantity Formula Unit Dimension
1. Heat (Q) Energy Joule [ML2 T −2 ]
