ReCaptcha 2.0: enable Submit button on callback if recaptcha successful

I have a very simple form as follows. I want to make it so that the Submit button is disabled, and only enabled after the user has successfully completed the ReCaptcha.

I'm assuming I'm going to need some Javascript / jQuery to do this.

Google's documentation on ReCaptcha 2.0 seems really sparse and dense (to me, anyway). I'd appreciate some pointers:

<form action="something.php" method="post">

Name: <input type="text" size="40" name="name">
<br>
<br>

<div class="g-recaptcha" data-sitekey="############-#####"></div>

<input type="submit" value="Submit" >

</form>