Question

Only sum of the radii of given pulleys is to be considered in

a) Open belt
b) crossed
c) None of the above​

Answer 1

Answer:

ᴛʜᴇ ɪɴᴇʀᴛɪᴀ ᴏꜰ ᴛʜᴇ ᴩᴜʟʟᴇy ɪꜱ ɪ=0.2 ᴋɢ−ᴍ2

ᴛʜᴇ ʀᴀᴅɪᴜꜱ ᴏꜰ ᴛʜᴇ ᴩᴜʟʟᴇy ɪꜱ ʀ=0.2 ᴍ

ᴛʜᴇ ꜱᴩʀɪɴɢ ᴄᴏɴꜱᴛᴀɴᴛ ᴏꜰ ᴛʜᴇ ꜱᴩʀɪɴɢ ɪꜱ ᴋ=50 ɴ/ᴍ,

ᴛʜᴇ ᴍᴀꜱꜱ ᴏꜰ ᴛʜᴇ ʙʟᴏᴄᴋ ᴄᴏɴɴᴇᴄᴛᴇᴅ ᴛᴏ ᴛʜᴇ ꜱᴩʀɪɴɢ ɪꜱ ᴍ=1 ᴋɢ

ᴛᴀᴋᴇ ɢ=10 ᴍꜱ2 ᴀɴᴅ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴛʜʀᴏᴜɢʜ ᴡʜɪᴄʜ ᴛʜᴇ ʙʟᴏᴄᴋ ᴅᴇᴄᴇɴᴅꜱ ɪꜱ ʜ=0.1 ᴍ

ᴛʜᴇ ꜱᴜᴍ ᴏꜰ ᴛʜᴇ ᴋɪɴᴇᴛɪᴄ ᴇɴᴇʀɢy ᴀᴛᴛᴀɪɴᴇᴅ ʙy ᴛʜᴇ ʙʟᴏᴄᴋ, ʀᴏᴛᴀᴛɪᴏɴᴀʟ ᴇɴᴇʀɢy ᴏꜰ ᴩᴜʟʟᴇy ᴀɴᴅ ᴛʜᴇ ꜱᴩʀɪɴɢ ᴩᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢy ᴡɪʟʟ ʙᴇ ᴇqᴜᴀʟ ᴛᴏ ᴛʜᴇ ʟᴏꜱꜱ ɪɴ ᴛʜᴇ ᴩᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢy ᴏꜰ ᴛʜᴇ ʙʟᴏᴄᴋ.

ᴛʜᴇ ᴀɴɢᴜʟᴀʀ ᴠᴇʟᴏᴄɪᴛy ᴏꜰ ᴛʜᴇ ᴩᴜʟʟᴇy ɪꜱ:

ω=ʀᴠ

=0.2ᴠ

ᴛʜᴇʀᴇꜰᴏʀᴇ ᴀᴩᴩʟyɪɴɢ ʟᴀᴡꜱ ᴏꜰ ᴄᴏɴꜱᴇʀᴠᴀᴛɪᴏɴ ᴏꜰ ᴇɴᴇʀɢy

ᴍɢʜ=21 ᴍᴠ2+21ɪω2+21 ᴋx2

⇒1×10×0.1=21×1×ᴠ2+21×0.2×0.04ᴠ2+21×50×0.01                             (x=ʜ)

⇒1=0.5 ᴠ2+2.5 ᴠ2+1/4

⇒3ᴠ2=43

⇒ᴠ=21=0.5 ᴍ/ꜱ

Answer 2

pulley is to be considered in open belt...not sure... but 80 percent it is correct...☺️