Question

I am not understand why 1/2mv2=mgh

Answer 1

1/2mv² = mgh

we have to check the correctness

by dimensional analysis

So LHS

Dimensional formula of 1/2mv²

will. be [M¹ L²T-²]

so now RHS

mgh

dimensional formula of mass is [M¹]

dimensional formula of g (acceleration due to gravity) is [ L¹ T-²]

dimensional formula of height(length) is [L¹]

so dimensional formula of mgh will be

= [M¹ L²T-² ]

so LHS = RHS

Answer 2

${\huge {\mathfrak {Answer :-}} }$

Energy always remains constant.

It can neither be created, nor be destroyed.

So, When is body is in motion, it has Kinetic energy, K. E. = 1/2 mv^2

And when the body is at rest, it has Potential energy, P. E. = mgh

Since, energy always remains constant.

So, 1/2 mv^2 = mgh

$\blue That's \: it$