the unit of time in that system in which the unit of length is 'metre'' , unit of mass ''kg' and unit of force ' kg wt ' is
1) 1 / √9.8 sec
2) (9.8)²sec
3)√9.8 sec
4) 9.8 sec

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Solution

$1 k g w e i g h t = 9.8 N I n t e r m s o f d i m e n t i o n s L E T [M_{1} L_{1} {T_{1}}^{- 2}] i s t h e d i m e n s i o n o f k g w e i g h t a n d [M_{2} L_{2} {T_{2}}^{- 2}] i s t h e d i m e n s i o n o f N . M_{1} = M_{2} = k g = M L_{1} = L_{2} = m e t e r = L n o w T_{1} a n d T_{2} a r e t h e d i f f e r e n t u n i t s o f t i m e . [M_{1} L_{1} {T_{1}}^{- 2}] = 9.8 [M_{2} L_{2} {T_{2}}^{- 2}] [M L {T_{1}}^{- 2}] = 9.8 [M L {T_{2}}^{- 2}] {T_{1}}^{2} = \frac{{T_{2}}^{2}}{9.8} T_{2} = s e c o n d T_{1} = \frac{s e c o n d}{\sqrt{9.8}} t h i s i s t h e n e w u n i t o f t i m e .$

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