# 125 same small drops are charged with 50 volt potential each. If they formed one big drop after mixing them, the potential of new big drop is

1. 50 V
2. 250 V
3. 500 V
4. 1250 V

## Answer (Detailed Solution Below)

Option 4 : 1250 V

## Detailed Solution

The correct answer is 1250 V.

Key Points

⇒ V1 = 4 π / 3 * R13 assuming spherical drops

⇒ V2 = 125 V1 = 4 pi / 3 * R23

⇒ V2 / V1  = 125 = R23R13

⇒ R2 / R1 = 1251/3 = 5

⇒ V1 = k Q1 / R1 electric potential of 1 drop

⇒ V2 = k Q2 / R2

⇒ V2 / V1 = (Q2 / Q1 ) * ( R1/ R2 ) = 125 / 5 = 25

⇒ V2 = 25 x V1 = 25 * 50 = 1250 V
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://testbook.com/question-answer/125-same-small-drops-are-charged-with-50-volt-pote--6078042ebb377ea54e2ab898", "fetch_time": 1675287614000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2023-06/segments/1674764499953.47/warc/CC-MAIN-20230201211725-20230202001725-00534.warc.gz", "warc_record_offset": 578589488, "warc_record_length": 73557, "token_count": 266, "char_count": 583, "score": 4.09375, "int_score": 4, "crawl": "CC-MAIN-2023-06", "snapshot_type": "latest", "language": "en", "language_score": 0.5503692626953125, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00051-of-00064.parquet"}