20m s - ] kmh - = m s - . Check the correctness of the following equation using dimensional analysis. Make a comment on it. S = ut + / at where s is the displacement, u is the initial velocity, t is the time and a is the acceleration produced.
Solution: Dimension for distance s = [L] Dimension for initial velocity v = [LT - ] Dimension for time t = [T] Dimension for acceleration a = [LT - ] - - - - Appendix [ML T - ] = K [M] a [LT - ] b By equating the dimensions, a = b = -b = - E = k.mc The value of constant k = E = mc This is Einstein’s mass energy relation . The velocity of a body is given by the equation v = b/t + ct +dt . Find the dimensional formula for b. Solution: (b/t) should have the dimensions of velocity b has the dimensions of (velocity x time) [b] = [LT ][ ] [ ] [ ] T L M LT .
The initial and final temperatures of a liquid in a container are observed to be . ± . ° C and . ± .
° C. Find the fall in the temperature of the liquid. Solution: t = ( . ± .
Solution: a) Among the two, the least number of significant after decimal is one = . = . b) The number of minimum significant figures is . × = .