Table of Units and Dimensions of Physical quantities.

Units & Dimensions of Physical quantities in S.I system.

Fundamental Physical Quantities:

 S.No Fundamental Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity 1. Mass Amount of matter in the object M kg 2. Length L meter 3. Time T sec 4. Electric current I or A ampere 5. Amount of substance N mole(mol 6. Luminous intensity J candela(cd) 7. Temperature K or $\theta$ Kelvin

Derived Physical Quantities:

 S.No Derived Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity 1. Area $l\times b$ [$latex{M^0L^2T^0}] $m^2$ 2. Volume $l\times b\times h$ [$M^0L^3T^o$] $m^3$ 3. Density $\frac{M}{V}$ [${M^1L^{-3}T^0$}] $kg/m^3$ 4. Specific Gravity $\frac{Density of Substance}{Density of Water}$ [$M^0L^0T^0$] No units 5. Frequency $\frac{no of vibrations}{Time}$ [$M^0L^0T^{-1}$] hertz 6. Angle $\frac{Arc}{radius}$ $M^0L^oT^o$ No units 7. Velocity $\frac{Displacement}{time}$ $M^0L^1T^{-1}$ m/sec 8. Speed $\frac{Distance}{time}$ $M^0L^1T^{-1}$ m/sec 9. Areal velocity $\frac{Area}{time}$ $M^0L^2T^{-1}$ $m^2sec^{-1}$ 10. Acceleration $\frac{Change in velocity }{time}$ $M^0L^1T^{-2}$ $m/sec^2$ 11. Linear momentum $M\times V$ $M^1L^1T^{-1}$ kg m/sec 12. Force $mass\times acceleration$ $M^1L^1T^{-2}$ kg-m/$sec^2$ or Newton 13. Weight w=mg $M^1L^1T^{-2}$ kg-m/$sec^2$ or Newton 14. Moment of force/Torque/Couple $Force\times arm$ $M^1L^2T^{-2}$ kg$m^2sec^{-2}$ 15. Impulse $Force\times time$ $M^1L^1T^{-1}$ kg m/sec or Ns 16. Pressure $\frac{Force}{Area}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 17. Work $Force\times Distance$ $M^1L^2T^{-2}$ Nm or Joule 18. Kinetic Energy $\frac{1}{2} mv^2$ $M^1L^2T^{-2}$ joule 19. Potential Energy mgh $M^1L^2T^{-2}$ joule 20. Gravitational constant $\frac{Force\times (Length)^2}{(mass)^2}$ $M^{-1}L^3T^{-2}$ $kg^{-1}m^3sec^{-2}$ 21. Gravitational field strength $\frac{Force}{mass}$ $M^0L^1T^{-2}$ $N kg^{-1}$ 22. Gravitational Potential $\frac{Work}{mass}$ $M^0L^2T^{-2}$ $J kg^{-1}$ 23. Force constant (k) $\frac{F}{L}$ $M^1L^0T^{-2}$ $N m^{-1}$ 24. Power $\frac{Work}{time}$ $M^1L^2T^{-3}$ W or J/sec 25. Moment of Inertia ( I ) $Mass\times Distance^2$ $M^1L^2T^{0}$ kg$m^2$ 26. Stress $\frac{Force}{Area}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 27. Strain $\frac{Change in length}{Origional length}$ $M^0L^0T^0$ No units 28. Modulus of Elasticity $\frac{Stress}{Strain}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 29. Poission’s Ratio σ =$\frac{Y}{2n}$-1 $M^0L^0T^0$ No units 30. Velocity gradient $\frac{Change in velocity}{Distance}$ $M^0L^0T^{-1}$ $sec^{-1}$ 31. Coefficient of dynamic viscosity $\frac{Tangential stress}{Velocity Gradient}$ $M^1L^{-1}T^{-1}$ kg$m^{-1}sec^{-1}$(or) N-sec/$latex  \m^2\$ (or)pascal-sec (or)poiseuille 32. Surface Tension $\frac{Force}{Length}$ $M^1L^0T^{-2}$ $kg sec^2$,N/m 33. Angular displacement ($\theta$) $\frac{Arc}{radius}$ $M^0L^oT^o$ no Units 34. Angular velocity(ω) $\frac{Angular displacement}{Time}$ $M^0L^oT^{-1}$ rad/sec 35. Angular acceleration(α) $\frac{Change in angular velocity}{Time}$ $M^0L^oT^{-2}$ rad/$sec^{-2}$ 36. Angular momentum Iω $ML^2T^{-1}$ $kg-m^2 sec^{-1}$ 37. Angular Impulse Iω $ML^2T^{-1}$ $kg-m^2 sec^{-1}$ 38. Temperature $\theta$ or K kelvin or degree Celsius 39. Coefficient of linear expansion(α) $\frac{l_2-l_1}{l_1\times Temp(t_2-t_1)}$ $M^0L^0T^0K^{-1}$ /kelvin 40. Specific heat $\frac{Energy}{Mass\times Temp}$ $M^0L^2T^{-2}K^{-1}$ 41. Latent heat $\frac{Energy}{Mass}$ $M^0L^2T^{-2}$ $joule-kg^{-1}$ 42. Entropy $\frac{Q}\theta$ $M^1L^2T^{-2}K^{-1}$ $J K^{-1}$ 43. Thermal capacity $\frac{H}\theta$ $M^1L^2T^{-2}K^{-1}$ $J K^{-1}$ 44. Gas constant $\frac{PV}{m T}$ $M^0L^2T^{-2}K^{-1}$ $joule-K^{-1}$ 45. coefficient of thermal conductivity $\frac{Qd}{A(\theta_2-\Theta_1)t}$ $M^1L^1T^{-3}K^{-1}$ $W m^{-1}K^{-1}$ 46. Pole strength $Ampere\times meter$ $M^0L^1T^0I$ Am 47. Magnetic Moment $M^0L^2T^0I^1$ $Amp-m^2$ 48. Magnetic flux $\phi$ $ML^2T^{-2}I^{-1}$ weber ;$T-m^{2}$ ;J/Amp 49. Magnetic field,magnetic flux density (B) $MT^{-2}I^{-1}$ Tesla;$J/A-m^{2}$ 50. Permeability of free space $\frac{\mu}{\mu_r}$ $MLT^{-2}I^{-2}$ $NA^{-2}$ 51. Magnetic susceptibilty also called volumetric or bulk susceptibility χm χm = μr − 1 $M^0L^oT^o$ no units 52. Electric Charge $I\times T$ $M^0L^0T^1I^1$ Amp sec , coul 53. Electric potential $\frac{Work}{Charge}$ $M^1L^2T^{-3}I^{-1}$ Volt 54. E.M.F $\frac{Work}{Charge}$ $M^1L^2T^{-3}I^{-1}$ Volt 55. Electric Capacity $\frac{q}{V}$ $M^{-1}L^{-2}T^4I^2$ Farad 56. Electric Resistance $\frac{V}{i}$ $M^1L^2T^{-3}I^{-2}$ Ohm (Ω) or volt/amp 57. Resistivity $\rho$ $\frac{R A}{L}$ $M^1L^3T^{-3}I^{-1}$ Ohm mt (Ω-m) 58. Conductivity $\sigma$ 1/$\rho$ $M^{-1}L^{-3}T^3I$ Siemens/m 59. Permittivity $\varepsilon$ $M^{-1}L^{-3}T^4I^2$ farad/m 60. Electric conductance $\frac{1}{R}$ $M^{-1}L^{-2}T^3I^2$ Siemens (or) mhos 61. Electric power $V\times I$ $M^1L^2T^{-3}I^{-1}$ Watt 62. Electrical Impedance(Z) $\frac{V}{i}$ $M^1L^2T^{-3}I^{-2}$ Ohm (Ω) or volt/amp 63. Electrical admittance 1/Z(Reciprocal of electric impedance) $M^{-1}L^{-2}T^3I^3$ Siemens (or) mhos 64. Self Inductance(L) $\displaystyle v=L\frac{di}{dt}$ $ML^2T^{-2}I{-2}$ weber/amp or Henry 65. Boltzmann’s constant $\frac{Energy}{Temp}$ $M^1L^2T^{-2}K^{-1}$ J/kelvin 66. Stefan’s constant $\frac{E}{At \theta^4}$ $M^1L^0T^{-3}K^{-4}$ $W m^{-2}K^{-4}$ 67. Co-efficient of friction $\mu$ $\mu$=$\frac{F}{N}$,N=Normal reaction dimension less scalar no units 68. Dielectric constant $\varepsilon_r$ It is also called relative permittivity dimension less no units 69. Planck’s constant $E=h\nu$ $ML^2T^{-1}$ J.sec (or) eV.sec 70. Refractive index μ $M^0L^oT^o$ no units 71. Focal length(f) Distance between center of the lens(mirror) to its focus L meter 72. Power of a lens (P) The reciprocal of the focal length of a lens in meters is called power of a lens; p=1/f $L^{-1}$ diaptors 73. Wave number No.of waves/distance $L^{-1}$ $m^{-1}$ 74. Wave length Length of a wave L meter

Important formulas in Physics.

Kinematics :

• Average Speed = $\frac{Totaldistancetraveled}{Total time taken}$
• If the body covers 1st half of distance with a speed x and the second half with a speed y,then the average speed = $\frac{2xy}{x+y}$
• If the body covers 1st 1/3rd of a distance with a speed x , and 2nd 1/3 with a speed y , and the 3rd 1/3rd distance with a speed z, then average speed =$\frac{3xyz}{xy+yz+zx}$
• Average velocity = $\frac{TotalDisplacement}{Total time taken}$
• If a body travels a displacement $s_1$ in $t_1$ seconds and a displacement $s_2$ in $t_2$ seconds, in the same direction then   Average velocity = $\frac{s_1+s_2}{t_1+t_2}$ .
• If a body travels a displacement $s_1$ with velocity $v_1$ , and displacement$s_2$ with velocity $v_2$ in the same direction then Average velocity = $\frac{( s_1 + s_2) v_1v_2}{s_1v_2+s_2v_1}$
• If a body travels first half of the displacement with a velocity $v_1$and next half of the displacement with a velocity $v_2$ in the same direction , then                                                          Average velocity = $\frac{2v_1v_2}{v_1+v_2}$ .
• If a body travels a time $t_1$ with velocity $v_1$ and for a time $t_2$ with a velocity $v_2$ in the same direction then Average velocity = $\frac{v_1t_2+V_2t_1}{t_1+t_2}$ .
• If the body travels 1st half of the time with a velocity $v_1$ next half of the time with a velocity $v_2$ in same direction , then  Average velocity = $\frac{v_1+v_2}{2}$
• For a body moving with uniform acceleration if the velocity changes from u to v in t seconds, then Average velocity = (u+v)/2 .
• Equations of motion of a body moving with uniform acceleration along straight line.
• a) V=u+at    b) S=ut+$\frac{1}{2}$$at^2$  c) $v^2$$u^2$ =2as
• Distance traveled  in the nth second    $s_n$=u+a(n-1/2)
• Equations of motion for a freely falling body ( Note: we can obtain these equations by substitution of u=0 and a=g in above equations . a) v=gt b) S=1/2 $gt^2$ c) $v^2$ = 2gs and the equation for the distance traveled in nth second changes to          $s_n$=g(n-1/2)
• Equations of motion of a body projected up vertically :(we will obtain these equations by substitution a=-g in equations of motion)
• a) v=u-gt  b) S=ut-1/2$gt^2$  c) $v^2-u^2$=-2gs and $s_n$=u-g(n-1/2)
• Equation for maximum height reached $H_{max}$ = $\frac{u^2}{2g}$ $\Rightarrow$ $H_{max} \alpha u^2$
• Time of ascent $t_a$=$\frac{u}{g}$;     $t_a$$\alpha$ u
• Time of descent  $t_d$ =$\frac{u}{g}$$t_d$ $\alpha$ u
• Time of flight T=2u/g
• When a body is thrown up from top of a tower or released from a rising baloon,with velocity u.Displacement traveled before reaching ground              S=-ut+1/2$gt^2$. (t= time during which the object is in the air and S=h=height of the tower).
• When a body is dropped from a tower of height h and another body is thrown up vertically with a velocity u then they will meet after t=h/u seconds.
• When a body is dropped from a tower of height h . Its velocity when it reaches ground v=$\sqrt(2gh)$
• If the displacements of a body in $m^{th} ,n^{th}$ seconds of its journey.Then the uniform acceleration of the body a=$\frac{s_n-s_m}{n-m}$
• From the above equation we can observe that by substituting n=1,2,3,4,…. we get a=$s_2-s_1$=$s_3-s_2$=……….. =$s_{n-s}s_{n-1}$ =a.
• A body projected up with velocity u from the top  of a tower reaches ground in $t_1$ seconds.If  it  is thrown down with the same velocity u it reaches ground in $t_2$ seconds.Then, when it is dropped freely the time taken to reach the ground will be t=$\sqrt(t_1t_2)$   and h=1/2 g$t_1t_2$   and $t_1 -t_2$ =2 $\frac{u}{g}$.
• Projectile motion :Let us suppose that a projectile is projected with an initial velocity u making an angle $\theta$ with x axis. a)Horizontal component of velocity $u_x = u cos\theta$ , and $u_x =v_x$ ,which will be constant through out the flight of the projectile as horizontal component of acceleration $a_x$ = 0.  b)Vertical component of velocity of the projectile $u_y = u sin\theta$. Vertical component of velocity at any time of its journey $v_y$ =$u_y$-gt or $v_y$ =$usin\theta$ -gt.   c)Magnitude of the resultant velocity V = $\sqrt(v_x^2+v_y^2)$  and the angle x made by v with the horizontal is given by $Tan\alpha$= $\frac{v_y}{v_x}$
• Time of ascent = $\frac{usin\theta}{g}$
• Time of descent = $\frac{usin\theta}{g}$
• Time of flight = $\frac{2u sin\theta}{g}$
• Maximum height reached  $H_{max}$ =$\frac{u^2 sin^2\theta}{2g}$ ;$\frac{H1}{H2}$ =$\frac{sin^2\theta_1}{sin^2\theta_2}$ when u is same
• Horizontal Range R= $\frac{(u^2sin2\theta)}{g }$=$\frac{2u^2 sin\theta cos\theta}{g}$  a)R is maximum when $\theta$ =$45^0$  b)$R_{max}$ =$\frac{u^2}{g}$  c) If T is the time of flight, R=$u cos\theta\times t$  d)For given velocity of projection R is same for the angles of projections $\theta$ and $(90-\Theta)$  Ex: 25 and 65 i.e the Range for those two angles will be same whose sum is $90^0$)