If 1 g cm s - 1 = x N s , then what is the value of x ?

Newton is the unit of force and dimension of newton is given by, MLT - 2 , 1 N = kg m s - 2 x N s = x kg m s - 1 , 1 kg = 1000 g , 1 m = 100 cm Here we have to convert Given quantity from CGS unit to MKS unit. Using dimensional analysis- n 2 M 2 L 2 T 2 - 1 = n 1 M 1 L 1 T 1 - 1 n 2 = n 1 M 2 M 1 L 2 L 1 T 2 T 1 - 1 ,where n 2 is value in MKS unit and n 1 is value in CGS unit. M 2 , L 2 and T 2 are in MKS unit while M 1 , L 1 and T 1 are units in CGS unit. Now, M 1 = 1 g , M 2 = 1000 g , L 2 = 100 cm , = L 1 = 1 cm , T 2 = 1 s , T 1 = 1 s , n 1 = 1 and n 2 = x x = 1 1000 1 100 1 1 - 1 ⇒ x = 10 - 5

With the usual notations, check if the following equation S t = u + 1 2 a 2 t - 1 is dimensionally correct or not.

Given, S t = distance travelled by the body in t th second. Dimensions of S t = L , a = LT - 2 , u = LT - 1 , and t = T By substituting the dimensions of each quantity, we can check the accuracy of the formula S t = u + 1 2 a 2 t - 1 ∴ L = LT - 1 + LT - 2 T ⇒ L = LT - 1 + LT - 1 Since the dimensions of left hand side and all the terms of right hand side are not equal, therefore, this equation is dimensionally incorrect . But after deriving this equation from kinematics, we can see that we've missed a term of 1 s multiplied to right hand side of the equation, which makes it dimensionally correct and can be used to solve numericals. S t = u × 1 s + 1 2 a 2 t - 1 × 1 s ∴ L = LT - 1 T + LT - 2 T T ⇒ L = L + L