If a fielder takes a catch and the ball touches the ground (ball is in hand only, but it’s touching the ground at the same time), is it considered as out?
If the condition is like this, A part of the ball is touching the ground when the catch is taken by the fielder,then the batsmen will not be given out. For a clean catch the no part of the ball should touch the ground .
For more details check this link.
Let's take a look at the laws of cricket.
Law 32 - 1 : Out Caught
The striker is out Caught if a ball delivered by the bowler [...] touches his bat without having previously been in contact with any fielder, and is subsequently held by a fielder as a fair catch before it touches the ground.
The above law (my emphasis) states that the ball must be held as a fair catch before it touches the ground.
If we now look at...
Law 32 - 3 : A fair catch
The act of making the catch shall start from the time when the ball in flight comes into contact with some part of a fielder’s person other than a protective helmet, and shall end when a fielder obtains complete control both over the ball and over his own movement.
A catch shall be considered to have been fairly made if [...] the ball does not touch the ground even though the hand holding it does so in effecting the catch.
In summary, the ball must be under complete control of the fielder before it touches the ground for it to be a fair catch.
In your question scenario, the ball is in the hand but touching the ground at the same time. In this situation, the umpire would decide which contact occurred first. (It could be a fraction of a second technically).
- Ball touched the ground before the catch. Not Out
- Ball touched the ground after the hand and the fielder had complete control. Out
- Ball touched the ground after the hand but the fielder did not have complete control. Not Out
In the applicance of this law, I have rarely seen a ball caught at exactly the same time as it touched the ground (for one would generally have the hand under the ball to catch it). In my experience the umpire would call not out as it is unlikely that the fielder would have complete control over the ball and his movement in such a scenario.
View the laws here.