Physics, asked by ppegu1658gmailcom, 8 months ago

Momentum is the production of mass and velocity if two bodies having ratio of their masses 1:2 and ratio of their momentum 2:1 then ratio of their velocities will be​

Answers

Answered by Anonymous
27

Given:

 \rm Ratio  \: of  \: masses \:  (m_1:m_2) = 1:2

 \rm Ratio \:  of \:  momentum \: (p_1:p_2) = 2:1

To Find:

 \rm Ratio  \: of \:  velocities \: (v_1:v_2)

Answer:

Momentum (p) of a body is measured as the product of mass (m) of the body and it's velocity (v) and has the same direction as that of the velocity.

 \boxed{ \boxed{ \bf{p = mv}}}

So,

 \rm \implies \dfrac{p_1}{p_2} = \dfrac{m_1v_1}{m_2v_2} \\  \\  \rm \implies \dfrac{2}{1} = \dfrac{1 \times v_1}{2 \times v_2}  \\  \\ \rm \implies \dfrac{ v_1}{ v_2} = \dfrac{2}{1}  \times \dfrac{2}{1}  \\  \\ \rm \implies \dfrac{ v_1}{ v_2} = \dfrac{4}{1} \\  \\\rm \implies  v_1 : v_2 = 4  : 1

 \therefore  \boxed{\mathfrak{Ratio  \: of \:  velocities \: (v_1:v_2) = 4:1}}

Answered by Anonymous
268

♣ Question :

ᴍᴏᴍᴇɴᴛᴜᴍ ɪꜱ ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛɪᴏɴ ᴏꜰ ᴍᴀꜱꜱ ᴀɴᴅ ᴠᴇʟᴏᴄɪᴛʏ ɪꜰ ᴛᴡᴏ ʙᴏᴅɪᴇꜱ ʜᴀᴠɪɴɢ ʀᴀᴛɪᴏ ᴏꜰ ᴛʜᴇɪʀ ᴍᴀꜱꜱᴇꜱ 1:2 ᴀɴᴅ ʀᴀᴛɪᴏ ᴏꜰ ᴛʜᴇɪʀ ᴍᴏᴍᴇɴᴛᴜᴍ 2:1 ᴛʜᴇɴ ʀᴀᴛɪᴏ ᴏꜰ ᴛʜᴇɪʀ ᴠᴇʟᴏᴄɪᴛɪᴇꜱ ᴡɪʟʟ ʙᴇ​

♣ According To Question :

ʀᴀᴛɪᴏ ᴏꜰ ᴍᴀꜱꜱᴇꜱ = 1 : 2

ʀᴀᴛɪᴏ ᴏꜰ ᴍᴏᴍᴇɴᴛᴜᴍ = 2 : 1

ʀᴀᴛɪᴏ ᴏꜰ ᴠᴇʟᴏᴄɪᴛɪᴇꜱ = ?

♣ Let :

ʀᴀᴛɪᴏ ᴏꜰ ᴍᴀꜱꜱᴇꜱ = m₁ : m₂

ʀᴀᴛɪᴏ ᴏꜰ ᴍᴏᴍᴇɴᴛᴜᴍ = p₁ : p₂

ʀᴀᴛɪᴏ ᴏꜰ ᴠᴇʟᴏᴄɪᴛɪᴇꜱ = v₁ : v₂

♣ Answer :

ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍᴀꜱꜱ × ᴠᴇʟᴏᴄɪᴛʏ

____________________________

\bf{p_1 :p_2=\dfrac{p_1}{p_2}}

\bf{v_1 :v_2=\dfrac{v_1}{v_2}}

\bf{m_1 :m_2=\dfrac{m_1}{m_2}}

____________________________

ᴀꜱ :- ᴍᴏᴍᴇɴᴛᴜᴍ = ᴍᴀꜱꜱ × ᴠᴇʟᴏᴄɪᴛʏ or p = mv

\bf{\dfrac{p_1}{p_2}=\dfrac{m_1\times v_1}{m_2\times v_2}

\bf{\dfrac{2}{1} = \dfrac{1 \times v_1}{2 \times v_2}}

\bf{\dfrac{2}{1} \times \dfrac{2 }{1} = \dfrac{v_1}{v_2}

\bf{ \dfrac{v_1}{v_2}=\dfrac{2}{1} \times \dfrac{2 }{1} }

\bf{ \dfrac{v_1}{v_2}=\dfrac{4}{1}}

\star\:\bf{ \dfrac{v_1}{v_2}=v_1:v_2}

\bf\dfrac{4}{1} = 4:1}

\star\:\bf{ \dfrac{v_1}{v_2}=4:1}

∴ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏꜰ ᴠᴇʟᴏᴄɪᴛɪᴇꜱ = 4 : 1

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