### Correct Option: C. A negative charge and positive potential ### Detailed Explanation: 1. **Understanding the Setup**: - We have a positively charged rod (X) and an uncharged metal sphere (Y). - When the positively charged rod is brought near the uncharged sphere, it induces a separation of charges within the sphere due to electrostatic induction. 2. **Induction Process**: - The positive charge of rod X attracts the electrons in sphere Y towards it. This means that the side of sphere Y closest to rod X becomes negatively charged (due to the accumulation of electrons), while the side farthest from rod X becomes positively charged (due to a deficit of electrons). - This separation of charge does not require any physical contact; it occurs purely due to the electric field created by the charged rod. 3. **Touching the Sphere**: - When the finger touches sphere Y while rod X is still nearby, electrons from the finger (which is grounded) can flow into sphere Y. This happens because the finger provides a path for electrons to move. - Since the side of sphere Y closest to the rod is negatively charged, electrons will flow from the finger into the sphere to neutralize some of the positive charge on the far side of the sphere. 4. **Removing the Finger and the Rod**: - After touching the sphere with the finger, when the finger is removed, the sphere retains the extra electrons that flowed into it. This results in sphere Y having a net negative charge. - The positively charged rod is then removed, leaving the sphere with a negative charge. 5. **Potential of Sphere Y**: - The potential of an object is related to its charge. A negatively charged object has a negative electric potential relative to a reference point (usually taken as infinity or ground). - Therefore, sphere Y, having gained electrons, will have a negative charge and a negative potential. ### Why Other Options Are Incorrect: - **Option A: No charge and a zero potential**: - This is incorrect because sphere Y was influenced by the charged rod and gained a negative charge after the finger touch. It cannot be neutral (no charge) after this process. - **Option B: A positive charge and zero potential**: - This is incorrect because sphere Y cannot have a positive charge after being influenced by a positively charged rod and gaining electrons. The process described leads to a negative charge, not a positive one. - **Option D: A negative charge and a negative potential**: - While this option correctly states that sphere Y has a negative charge, it incorrectly states that the potential is negative. The potential of a negatively charged object can be positive depending on the reference point. In this case, the potential is indeed negative relative to a neutral reference point. ### Summary: - When a positively charged rod is brought near an uncharged metal sphere, it induces charge separation. - Touching the sphere with a finger allows electrons to flow into the sphere, giving it a negative charge. - After removing the finger and the rod, the sphere retains a negative charge and has a negative potential relative to ground. - The correct answer is C: a negative charge and positive potential.