Question

15. Galileo's law of odd numbers reflects that a particle
starting from rest with uniform acceleration covers
distance (in equal time intervals in straight line
motion) in the ratio
(1) 1:2:3:4
(2) 1:1:1:1
(3) 1:2:4:8 (4) 1:3 5:7​

Answer 1

Answer:

( 4 ).

Explanation:

As the rule says 'odd number law' it contains only odd numbers.

However, if you are in need of a proof for this :

Particle which was initially at rest starts moving with a uniform acceleration a and at time t its velocity is v and displacement till now is S.

Using the equations of motion :

= > S = ut + ½ at^2 { u is the initial velocity, in this cases u = 0 }

= > S = 0 + ½ at^2

= > S = ½ at^2

At t = 1, S' = ½ a

At t = 2, S'' = ½ a( 2 )^2 = 4 ( ½ S )

Displaced by S'( 4 - 1 ) = 3S'

At t = 3, S'" = ½ a( 3 )^2 = 9S'

Displaced by ( 9 - 4 ) S' = 5S'

Displacement travelled by the body during equal time intervals are in ratio of 1 : 3 : 5 so on.