Question

7. Which of the following relations is dimensionally incorrect? * (a) ½ mv² = mgh (b) K = m²v³ (c) W = ½ mv² – ½ mu² (d) T = √(l/g)​

Answer 1

Explanation:

A> We know acceleration a=rate of change of velocity

a=tv−u where v=final velocity and u = initial velocity and t= time

Thus we can rewrite the above equation as,

u=v−at

[LT−1]=[LT−1]−[LT−2][T]

[LT−1]=[LT−1]       (Dimensionally correct)

B> From equation of motion we get displacement

s=ut+21at2

s−ut=21at2

[L]−[LT−1][T]=[LT−2][T2]

Here also, LHS =RHS

C>The equation u2=2a(gt−1)

Substituting the dimensions:

[LT−1]2=[LT−2]([LT−2][T])

[L2T−2]=[L2T−3]

LHS is not equal to RHS.

D> From equation of motion,

v2=u2+2as

v2−u2=2as

[LT−1]2−