Planck Time Problem: Calculation & Explanation

[Sagari]

Homework Statement

Hi Guys,
Just started a Mechanical Engineering Course and in my Physics this came up, I'm really confused and don't know were to start. I was wondering if anyone could shed any light on the subject. Thanks guys.

Three of the fundamental constants of physics are the speed of light, c = 3.0 × 10⁸ m/s, the universal gravitational constant, G = 6.7 × 10ˉ¹¹m³·kgˉ¹·sˉ², and Planck’s constant,
h = 66 × 10ˉ³⁴kg·m²·sˉ¹.
Find a combination of these three constants that has the dimensions of time. The time is called Planck time and represents the age of the universe before which the laws of physics as presently understood cannot be applied.
Using the formula for the Planck time derived in part (a), what is the time in seconds?

Homework Equations

The Attempt at a Solution

 

[PeterO]

Homework Statement

Hi Guys,
Just started a Mechanical Engineering Course and in my Physics this came up, I'm really confused and don't know were to start. I was wondering if anyone could shed any light on the subject. Thanks guys.

Three of the fundamental constants of physics are the speed of light, c = 3.0 × 10⁸ m/s, the universal gravitational constant, G = 6.7 × 10ˉ¹¹m³·kgˉ¹·sˉ², and Planck’s constant,
h = 66 × 10ˉ³⁴kg·m²·sˉ¹.
Find a combination of these three constants that has the dimensions of time. The time is called Planck time and represents the age of the universe before which the laws of physics as presently understood cannot be applied.
Using the formula for the Planck time derived in part (a), what is the time in seconds?

Homework Equations

The Attempt at a Solution

If you multiply G by h, the units are (m³·kgˉ¹·sˉ²) x (kg·m²·sˉ¹)

this gives

kg⁰·m⁵·sˉ³

which isn't seconds, but at least the kg has gone!

Use the right amount of the quantities and you will be left with just seconds, presumably.

EDIT: there was no real reason why I chose G and H to start with - but I had to chose a couple of them to show what happens.

 

[Sagari]

If you multiply G by h, the units are (m³·kgˉ¹·sˉ²) x (kg·m²·sˉ¹)

this gives

kg⁰·m⁵·sˉ³

which isn't seconds, but at least the kg has gone!

Use the right amount of the quantities and you will be left with just seconds, presumably.

EDIT: there was no real reason why I chose G and H to start with - but I had to chose a couple of them to show what happens.

Ok mate thanks for the help