Question

The distance x covered by a particle is time to is given by
x = at+bt^2+ct^3+d+4
Calculate the dimensions by a/b and c/d.

Please help me!!!​

Answer 1

Answer:

0, 0, 1

0, 0, -1/3

Explanation:

For question to be true, dimension of 4 unit must [L].

x = at + bt^2 + ct^3 + d + 4metre

When two quantities are related by =, +, -, they have same dimensional formula.

=> [x] = [at] = [bt²] = [ct³] = [d]

=> [x] = [a][t] = [b][t²] = [c][t³] = [d]

Therefore,

(i): [a][t] = [b][t²] → [a]/[b] = [t²]/[t] = [T^1]

(ii): [c][t³] = [d] → [c]/[d] = 1/[t³] = [T^(-1/3)]

Hence,

(i): Dimension formula of a/b = [a/b]

= [a]/[b] = [T^1] = [M^0 L^0 T^1]

(ii): Dimension formula of c/d = [c/d]

= [c]/[d] = [T^(-1/3)] = [M^0 L^0 T^(-1/3)]

Therefore,

Dimensions of a/b are 0, 0, 1

Dimensions of c/d are 0, 0, -1/3