Question

bodies masses 5 kg and 10 kg moving with same momentum then ratio of their kinetic energy​

Answer 1

Answer

Ratio of kinetic energies is 2 : 1

Given

Bodies of masses 5 kg and 10 kg moving with same momentum

To Find

Ratio of kinetic energies

Concept Used

We need to find the relation b/w K.E , mass and momentum . For that ,

$\rm K.E=\dfrac{1}{2}mv^2\\\\\to \rm K.E=\dfrac{mv^2}{2}\\\\\to \rm K.E=\dfrac{(mv)^2}{2m}\ \{\bf{\because\ \div m\ on\ num\ and\ denom\ }\}\\\\\to \bf K.E=\dfrac{P^2}{2m}$

where ,

• K.E denotes Kinetic energy
• P denotes momentum
• m denotes mass of the body

Solution

Here , we need to find the ratio of their kinetic energies having masses 5 and 10 kg's with same momentum ,

$\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{\frac{P^2}{2m_1}}{\frac{P^2}{2M_2}}\\\\\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{P^2}{2m_1}\times \dfrac{2m_2}{P^2}\\\\\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{m_2}{m_1}$

Given , m₁ = 5 kg and m₂ = 10 kg

$\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{10}{5}\\\\\to \bf \dfrac{K.E_1}{K.E_2}=\dfrac{2}{1}\ \; \bigstar$

Answer 2

Answer:

Answer

Ratio of kinetic energies is 2 : 1

Given

Bodies of masses 5 kg and 10 kg moving with same momentum

To Find

Ratio of kinetic energies

Concept Used

We need to find the relation b/w K.E , mass and momentum . For that ,

\begin{gathered}\rm K.E=\dfrac{1}{2}mv^2\\\\\to \rm K.E=\dfrac{mv^2}{2}\\\\\to \rm K.E=\dfrac{(mv)^2}{2m}\ \{\bf{\because\ \div m\ on\ num\ and\ denom\ }\}\\\\\to \bf K.E=\dfrac{P^2}{2m}\end{gathered}

K.E=

2

1

mv

2

→K.E=

2

mv

2

→K.E=

2m

(mv)

2

{∵ ÷m on num and denom }

→K.E=

2m

P

2

where ,

K.E denotes Kinetic energy

P denotes momentum

m denotes mass of the body

Solution

Here , we need to find the ratio of their kinetic energies having masses 5 and 10 kg's with same momentum ,

\begin{gathered}\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{\frac{P^2}{2m_1}}{\frac{P^2}{2M_2}}\\\\\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{P^2}{2m_1}\times \dfrac{2m_2}{P^2}\\\\\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{m_2}{m_1}\end{gathered}

→

K.E

2

K.E

1

=

2M

2

P

2

2m

1

P

2

→

K.E

2

K.E

1

=

2m

1

P

2

×

P

2

2m

2

→

K.E

2

K.E

1

=

m

1

m

2

Given , m₁ = 5 kg and m₂ = 10 kg

\begin{gathered}\to \rm \dfrac{K.E_1}{K.E_2}=\dfrac{10}{5}\\\\\to \bf \dfrac{K.E_1}{K.E_2}=\dfrac{2}{1}\ \; \bigstar\end{gathered}

→

K.E

2

K.E

1

=

5

10

→

K.E

2

K.E

1

=

1

2

★