Question

# A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.

A

3F7m,2F7m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

2F7m,3F7m

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

4F7m,3F7m

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

3F7m,4F7m

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A 3F7m,2F7m For the cyclinder, F2−f=ma1 ...(i) Taking moment of forces about C fR=Iα ⇒f=mRα2(∵ I=mR22) .......(ii) For the plank, F2+f=(2m)a2 ......(iii) And at the point of contact P, the acceleration of the two bodies must be same a1−Rα=a2 .....(iv) from (i)and(ii),(iii)and(iv)F=(ma1+2ma2),andF2+mRα2=2ma2 substititing value of α and solving for a1 and a2, we get acceleration of plank, a2=2F7m,and acceleration of cyclinder, a1=3F7m

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Problems
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program
{"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://byjus.com/question-answer/a-solid-cylinder-of-mass-m-and-radius-r-rests-on-a-plank-of-mass-3/", "fetch_time": 1709224334000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-10/segments/1707947474843.87/warc/CC-MAIN-20240229134901-20240229164901-00153.warc.gz", "warc_record_offset": 142798552, "warc_record_length": 33096, "token_count": 447, "char_count": 1382, "score": 3.515625, "int_score": 4, "crawl": "CC-MAIN-2024-10", "snapshot_type": "latest", "language": "en", "language_score": 0.8464179039001465, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00059-of-00064.parquet"}