Question

A stone is thrown upwards from the ground with a velocity ‘u’.

1. What is the maximum height attained by the stone?

2. Check the correctness of the equation obtained in (a) using the method of dimensional analysis.

Answer 1

1. H = \(\frac{u^2}{2g}\) ___(1)

u = u, v = o, a = -g, h = ?

We can find maximum height using the equation

u² = u² + 2as

0 = u² + 2 × -g × H

2gh = u²

H = \(\frac{u^2}{2g}\)

2. Dimension of H = L

Dimension of u = (LT^-1)

Dimensions of time (t) = T

Dimension of g = (LT^-2)

substituting these values in equation (1) we get

L = \(\frac{(LT^{-1})^2}{LT^{-2}}\)

L = L.