Problem Statement:
A charged sphere of radius 3 cm with a charge of 2 μC is touched with a neutral sphere of radius 5 cm. We need to determine the charge acquired by the neutral sphere.

Solution:
To solve this problem, we can use the principle of charge conservation. According to this principle, the total charge before and after the spheres are touched remains the same.

Step 1: Calculating the initial charge of the charged sphere:
The charge of the charged sphere is given as 2 μC.

Step 2: Calculating the final charge of the charged sphere:
When the charged sphere is touched with the neutral sphere, some charge is transferred between the spheres. As a result, both spheres acquire the same charge.

Since the neutral sphere initially has no charge, it acquires some charge from the charged sphere. Let's assume the charge acquired by the neutral sphere is Q.

The final charge of the charged sphere can be calculated using the equation:
Initial charge of the charged sphere - Charge acquired by the neutral sphere = Final charge of the charged sphere

2 μC - Q = Final charge of the charged sphere

Step 3: Applying the principle of charge conservation:
According to the principle of charge conservation, the total charge before and after the spheres are touched remains the same. Therefore, the sum of the initial charges of both spheres should be equal to the sum of their final charges.

Initial charge of the charged sphere + Initial charge of the neutral sphere = Final charge of the charged sphere + Final charge of the neutral sphere

2 μC + 0 = Final charge of the charged sphere + Q

Step 4: Solving the equations:
By equating the equations from steps 2 and 3, we can solve for the final charge of the charged sphere and the charge acquired by the neutral sphere.

2 μC - Q = 2 μC + Q

Simplifying the equation, we get:

-Q = Q

2Q = 0

Q = 0

Therefore, the charge acquired by the neutral sphere is 0. The neutral sphere remains neutral after being touched with the charged sphere.

Conclusion:
The neutral sphere does not acquire any charge when touched with the charged sphere. Its charge remains 0, and it stays neutral.