Question

Two particle having mass M and m are moving in a circular path having are same R and r . If the time periods are same than what is the ratio of their angular velocity.​

Answer 1

ᴄᴏʀʀᴇᴄᴛ ǫᴜᴇsᴛɪᴏɴ :-

$\green{★}$Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same, than what is the ratio of their angular velocity?

ɢɪᴠᴇɴ :-

$\green{★}$Two particles having mass M and m are moving in a circular path having radius R and r.

ᴛᴏ ғɪɴᴅ :-

$\green{★}$What is the ratio of their angular velocity.

sᴏʟᴜᴛɪᴏɴ :-

${\boxed{{\bf{{★}Time \: period \: of \: revoloution\: ➯\:T_{1} = {T}_{2} }}}}$

$\orange{★}$ According to the question :-

${\bf\large</u></strong><strong><u>\</u></strong><strong><u>r</u></strong><strong><u>e</u></strong><strong><u>d</u></strong><strong><u>{</u></strong><strong><u>→</u></strong><strong><u> {</u></strong><strong><u>T</u></strong><strong><u>}</u></strong><strong><u>_</u></strong><strong><u>{1} = {</u></strong><strong><u>T</u></strong><strong><u>}</u></strong><strong><u>_</u></strong><strong><u>{2} }}$

${\bf\large</u></strong><strong><u>\</u></strong><strong><u>r</u></strong><strong><u>e</u></strong><strong><u>d</u></strong><strong><u>{</u></strong><strong><u>∴</u></strong><strong><u> \frac{2\pi}{ {w}</u></strong><strong><u>_</u></strong><strong><u>{1} } = \frac{2\pi}{ {w}</u></strong><strong><u>_</u></strong><strong><u>{2} } }}$

${\bf\large</u></strong><strong><u>\</u></strong><strong><u>r</u></strong><strong><u>e</u></strong><strong><u>d</u></strong><strong><u>{</u></strong><strong><u>→</u></strong><strong><u> {w}</u></strong><strong><u>_</u></strong><strong><u>{1} = {w}</u></strong><strong><u>_</u></strong><strong><u>{2} }}$