Question

The masses of two bodies A and B are in the ratio of 2:3. They are movin with velocities of 45 m/s and 15 m/s respectively. What is the ratio of their
kinetic energies?​

Answer 1

Given :

The masses of two bodies A and B are in the ratio of 2:3 . They are moving with velocities of 45 m/s and 15 m/s respectively

To Find :

Ratio of their kinetic energies

Solution :

Kinetic energy is given by ,

$\bigstar\ \; \sf K.E=\dfrac{1}{2}mv^2$

where ,

• K.E denotes Kinetic energy
• m denotes mass
• v denotes velocity

_________________________

Given ,

Velocity of body A = 45 m/s

Velocity of body B = 5 m/s

Ratio of masses of bodies A and B = 2:3

$\to \sf \dfrac{K.E_A}{K.E_B}=\dfrac{\frac{1}{2}m_A.v_A^2}{\frac{1}{2}m_B.v_B^2}\\\\\to \sf \dfrac{K.E_A}{K.E_B}=\dfrac{m_A}{m_B}.\left(\dfrac{v_A}{v_B}\right)^2\\\\\to \sf \dfrac{K.E_A}{K.E_B}=\dfrac{2}{3}.\left(\dfrac{45}{15}\right)^2\\\\\to \sf \dfrac{K.E_A}{K.E_B}=\dfrac{2}{3}.(3)^2\\\\\leadsto \sf \pink{\dfrac{K.E_A}{K.E_B}=\dfrac{6}{1}}\ \; \bigstar$

So , K.Eₐ : K.E₈ = 6 : 1

Answer 2

Answer:

Ratio of their kinetic energies is 6 : 1.

Explanation:

Given that,

• The masses of two bodies A and B are in the ratio of 2:3.
• Velocity of first body ($K.E_A$) = 45 m/s.
• Velocity of second body ($K.E_B$) = 15 m/s.

As we know that,

$\sf{ \bigstar\: K. E \: = \: \frac{1}{2} mv^2}$

According to Question,

$\hookrightarrow \: {\sf\frac{ K.E_A}{K.E_B} = \frac{ \frac{1}{2} \times m_Av {}^{2}_A }{ \frac{1}{2} \times m_Bv {}^{2}_B } }$

$\hookrightarrow \: {\sf\frac{K.E_A}{K.E_B} = \frac{ \cancel{\frac{1}{2}} \times m_Av {}^{2}_A }{ \cancel{\frac{1}{2}} \times m_Bv {}^{2}_B } }$

$\hookrightarrow \: {\sf\frac{K.E_A}{K.E_B} = \frac{ m_A \times v {}^{2}_A }{{m_B} \times {v {}^{2}_B }}}$

$\hookrightarrow \: {\sf\frac{ K.E_A}{K.E_B} = \frac{ 2\times 45 {}^{2} }{{3} \times {15 {}^{2} }}}$

$\hookrightarrow \: {\sf\frac{K.E_A}{K.E_B} = \frac{ \cancel{4050}}{{} { \cancel{675}}}}$

$\hookrightarrow \: { \boxed{ \red { \sf{ K.E_A \ratio K.E_B = 6 \ratio 1}}}} \: \bigstar$