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Vishrant Vasavada Grade: 11
        If power P, length L and time T are chosen as base quantities, give dimensional formula of mass.
7 years ago

Answers : (2)

AskIITians Expert Hari Shankar IITD
17 Points
										

Power P =


Work / Time = Force * distance/ TIme


= mass *  accelaration * distance/Time


= mass * (distance/time2) * distance/time


= mass * distance3 * time-3


Therefore, [P] = [ML3T-3]


Let mass M be PxLyTz .


Hence, M = [ML3T-3]xLyT= MxL(3x+y)T(-3x+z)


Write the LHS as M1L0T0. Then, by comparing the exponents on both sides, we get 3 equations :


x = 1..............(1)


3x+y = 0................(2)


-3x+z = 0...................(3)


Using (1) in (2), y = -3


Using (1) in (3), z=3.


Therefore, M = P1L-3T3


 

7 years ago
AskiitianExpert Shine
10 Points
										

Hi


units of P = W = kg.m^2/s^3

             L = m

             T = s


For getting the dimensional formula for mass (kg) assume :

   P^p L^l T^t = kg


putting the units in place of P, L and T

   (kg.m^2/s^3)^p m^l s^t = kg

 

Comparing the units on LHS and RHS :

 (for kg) p=1

(for s) -3p+t = 0

               t = 3p = 3

(for m) 2p + l=0

              l = -2p = -2


Then we get the formula as : [P] [L]^-2 [T]^3 = kg

7 years ago
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