Question

if a radius of orbit of revolution becomes nine times<br />then time period becomes n times. What is the value of X.​

Answer 1

Aɴsᴡᴇʀ:

• The required vale of x = 27

Gɪᴠᴇɴ:

• If a radius of orbit of revolution becomes nine times then time period becomes x times.

Nᴇᴇᴅ Tᴏ Fɪɴᴅ:

• The required value of x = ?

Solution:

Let,

• The time 1 = T
• The time 2 = Tx

• The radius 1 = R
• The radius 2 = 9R

Bʏ ᴜsɪɴɢ ᴛʜᴇ Kᴇᴘʟᴇʀ's ᴛʜɪʀᴅ ʟᴀᴡ ᴡᴇ ɢᴇᴛ:

• T² ∝ R³

• ${\underline{\boxed{\sf{\dfrac{(Time\:1)^2}{(Time\:2)^2} = \dfrac{(Radius\:1)^3}{(Radius\:2)^3} }}}}$

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Pᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇs:

$\longrightarrow \sf {\dfrac{T^2}{(Tx)^2} = \dfrac{R^3}{9R^3}}$

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$\longrightarrow \sf {\dfrac{1}{x^2} = \dfrac{1}{9^3}}$

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$\longrightarrow \sf {x^2 = 729}$

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$\longrightarrow \boxed{\sf{\purple{x = 27}}}$

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Tʜᴇʀᴇғᴏʀᴇ:

• The required value of x is 27.

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