c) The lowest least number of significant digit after decimal is one . + . = . Rounding off we get .
d) The lowest least number of significant digit after decimal is one . +. = . = .
. Arrive at Einstein’s mass-energy relation by dimensional method (E = mc ) Solution: Let us assume that the Energy E depends on mass m and velocity of light c. E a m a c b E = km c a b where K a constant Dimensions of E = [ML T - ] Dimensions of m = [M] Dimensions of c = [LT - ] Substituting the values in the above equation - - - - Appendix . A capacitor of capacitance C = F is charged to a voltage of V = ± .
Volt . Calculate the charge Q [Use Q= CV] Solution: (C + D C) = ( . ± . ) m f (V + D V) = ( ± .
) V Q = CV Q = . × - × = × - coulomb Error in C C C Error in V V V Error in Q = Error in C + Error in V = . % + . % = .
% ∴ Charge Q = ( × - ± . %) coulomb SOLVED EXAMPLE UNIT- . The position vector for a particle is represented be ˆ t i tj k , find the velocity and speed of the particle at t = sec? Solution: dr dt = ti j The velocity at any time ‘ t ’ is given by ti j The magnitude of velocity is speed.
The speed at any time ‘ t ’ is then given by . % . Two resistors of resistances R = ± Ohm and R ± Ohm are connected in parallel combination. Calculate the equivalent resistance.
Hint: ′ = Solution: The