Saved Bookmarks
| 1. |
(ncert): A Famous Relation In Physics Relates ‘moving Mass’ M To The ‘rest Mass’ Mo Of A Particle In Terms Of Its Speed V And The Speed Of Light, C. (this Relation First Arose As A Consequence Of Special Relativity Due To Albert Einstein). A Boy Recalls The Relation Almost Correctly But Forgets Where To Put The Constant C. He Writes? |
|
Answer» Dimension of m (MASS) = [M1L0T0] Dimension of m0 (mass) = [M1L0T0] Dimension of V (velocity) = [M0L1T-1] ∴ Dimension of v2= [M0L2T-2] Dimension of c (velocity) = [M0L1T-1] Applying principle of HOMOGENEITY of dimensions, [LHS] = [RHS] = [M1L0T0] ⇒ The equation (1- v2)½ must be dimension less, which is possible if we have the expressions as: (1 – v2/c2) The equation after placing ‘c’ Dimension of m (mass) = [M1L0T0] Dimension of m0 (mass) = [M1L0T0] Dimension of v (velocity) = [M0L1T-1] ∴ Dimension of v2= [M0L2T-2] Dimension of c (velocity) = [M0L1T-1] Applying principle of homogeneity of dimensions, [LHS] = [RHS] = [M1L0T0] ⇒ The equation (1- v2)½ must be dimension less, which is possible if we have the expressions as: (1 – v2/c2) The equation after placing ‘c’ |
|