Question

57. Acceleration (a), velocity (1) and displacement (X)
are related according to equation a=v/A+x/B
Dimension of time in dimensional formula of AB is
(where A and B are constants)
​

Answer 1

answer : dimension of AB = [T³]

explanation : acceleration (a), velocity (v) and displacement (x) are related according to equation, a = v/A + x/B

from dimensional analysis,

dimension of a = dimension of (v/A) = dimension of (x/B)

case 1 : dimension of a = dimension of (v/A)

or, [LT-²] = dimension of v/dimension of A

or, [LT-²] = [LT-¹]/dimension of A

or, dimension of A = [LT-¹]/[LT-²] = [T]

case 2 : dimension of a = dimension of (x/B)

or, [LT-²] = dimension of x/dimension of B

or, [LT-²] = [L]/dimension of B

or, dimension of B = [L]/[LT-²] = [T²]

so, dimension of AB = [T] × [T²] = [T³]