Question

Write the dimension a/b in the relation E = (b - x 2 ) / at , where E is energy, x is distance and t is time. Please show the method to solve this question.

Answer 1

E = ( b -x²) /at
= ( b/at - x²/at)

where E = energy
t = time
x = displacement.

so,

dimension of E = dimension of { b/at }
b/at = E

b/a = Et

dimension of {a/b} = 1/Et = 1/[ ML²T-²][ T]

= [ M-¹ L-²T]

Answer 2

Answer:

The dimension of a and b are [M^-1T^1] and [ML^2T^-2].

Give the relation as,

e= b-x^2 / at

Here

E = energy

X = distance

t = time

we know that.

The dimension formula

e = [ML^2T^-2]

x = [L]

t = [T]

using principle of homogenecty

e = b.. (1)

[ML^2T^-2] = b

e = x^2 / at .. (2)

at = x^2 / e

at = [L^2] / [ML^2T^-2]

at = [M^-1 T^2]

a = [M ^-1 T^2] / T

Hence the dimension of a and b are [M^-1T^1] [ML^2T^-2].

hopethis helps you