on brew day of my first batch, when i was ready to take OG reading, i dropped my hydrometer so no OG.
Is there a way to get a rough estimate of the OG. Thanks
Yes, but it is expensive to buy the toys, as M__ said. To send the beer away for tests is also expensive.
In the words of the great Charlie Papazian: Relax, don't worry, have a homebrew.
OG is not important. FG is important as it will help confirm that your beer has finished fermenting.
Go to your local homebrew store and get two hydrometers. :)
I hope you did not drop the hyrometer into your beer! O_o
Digital alcohol meters exist to replace hydrometers, but they are not cheap.
What I would do instead, if brew day is not too far gone, is rush to the store to get a new hydrometer and measure approximatively from there. Watch out though, if you don't want oxygen reaching your brew, this is a bad idea.
Another alternative is to try to estimate the OG. This calculator says it does so: http://www.brewersfriend.com/allgrain-ogfg/
I've never used it in practice, I can't tell if it's right from experience.
Contrary to popular opinion, you don't need a hydrometer like you need sanitizer. You use a hydrometer to find out how efficiently sugars were extracted from your grains. Since you likely used extract, that's built into the recipe (it should be listed). You'll probably want something to check to see if the fermentation has completed by verifying that the gravity doesn't change for a few days in a row (normally, the advise is 3 day), but that's not a huge deal either. Let the fermentation go for 14 days if it's ale and you should be fine (provided that you're fermenting at ale temperatures). Now, that's like watching the leaves move and figuring which way the wind is blowing. It doesn't give you much information and it doesn't really tell you what you need to know.
Here's what I would do if I were you... if homebrewing is going to be a hobby that you think you're going to enjoy for a while, go on that very popular auction website and look for a brewing refractometer. They're bigger than a hydrometer so you won't be tempted to put it in your pocket and they're easier to use. A couple of drops will tell you your gravity and you don't have to get it to 70 degrees. If you ever looked to a toilet paper tube when you were a a kid, you can use a refractometer.