**Solution:**

To solve this problem, we need to analyze the motion of the man and the stone separately.

**Motion of the Man:**

Since the man is in a gravity-free space, there is no force acting on him, and therefore he remains stationary at a height of 10m above the floor throughout the entire process. The distance of the man above the floor will be **10m**.

**Motion of the Stone:**

To determine the distance of the stone above the floor when it reaches the floor, we can use the equations of motion.

Let's assume the initial position of the stone is at the same height as the man, which is 10m above the floor. The initial velocity of the stone is given as 2m/s in the downward direction, and the acceleration due to gravity is approximately 9.8m/s² acting in the downward direction.

Using the equation of motion:

**s = ut + (1/2)at²**

Where:
- s = distance traveled
- u = initial velocity
- t = time taken
- a = acceleration

We can calculate the time taken for the stone to reach the floor:

s = 0 (since the stone reaches the floor)
u = 2m/s (initial velocity)
a = 9.8m/s² (acceleration due to gravity)

0 = 2t + (1/2)(9.8)t²

0 = 2t + 4.9t²

0 = t(2 + 4.9t)

Either t = 0 or 2 + 4.9t = 0

The time taken cannot be zero since the stone needs time to reach the floor. Therefore, we solve the second equation:

2 + 4.9t = 0

4.9t = -2

t = -2/4.9 ≈ -0.408s

Since time cannot be negative, we discard this solution.

Therefore, the time taken for the stone to reach the floor is approximately 0.408s.

Using the equation of motion to find the distance traveled by the stone:

s = ut + (1/2)at²

s = 2(0.408) + (1/2)(9.8)(0.408)²

s ≈ 0.816 + 0.816 ≈ 1.632m

Therefore, the distance of the stone above the floor when it reaches the floor is approximately **1.632m**.

**Conclusion:**

The distance of the man above the floor remains constant at **10m** throughout the process. The distance of the stone above the floor when it reaches the floor is approximately **1.632m**. Therefore, the correct option is **(4) 10m**.

M1=mass of man= 50kg.V2=velocity of stone = 2m/s.M2=mass of stone = 0.5 kg .we can apply law of conservation of momentum,M1 V1=M2V2.50×V=0.5×2.25×V=0.5.V=0.5/25=1/50=0.02m/s.V=0.02m/s is the velocity of man.the time taken by the stone is V=S/t .given height is 10m.t=S/V .t=10/2=5.distance moved by man is.v=s/t.s=vt .s=0.02×5=0.1m.total distance of man above floor is =10+0.1=10.1m.