Question

Two bodies of masses 2 kg and 5 kg respectively are moving at same velocity . The ratio of their kinetic energy will be​

Answer 1

Given:

Mass of two bodies:

$\rm m_1 = 2 kg \\ \rm m_2 = 5 kg$

Velocities of both the bodies are same:

$\rm v_1 = v_2 = v$

To Find:

Ratio of their kinetic energy $\sf (KE_1 : KE_2)$

Answer:

Kinetic energy:

$\boxed{ \boxed{ \bf{KE = \dfrac{1}{2} m {v}^{2} }}}$

v → Velocity of the body

m → Mass of the body

So,

$\rm \implies \dfrac{KE_1}{KE_2} = \dfrac{ \cancel{ \dfrac{1}{2}} m_1 v_1}{\cancel{ \dfrac{1}{2}}m_2v_2} \\ \\ \rm \implies \dfrac{KE_1}{KE_2} = \dfrac{ m_1 \cancel{v}}{m_2\cancel{v}} \\ \\ \rm \implies \dfrac{KE_1}{KE_2} = \dfrac{ m_1 }{m_2} \\ \\ \rm \implies \dfrac{KE_1}{KE_2} = \dfrac{2 }{5} \\ \\ \rm \implies KE_1 : KE_2 = 2 : 5$

$\therefore$ $\boxed{\mathfrak{Ratio \ of \ their \ kinetic \ energy \ (KE_1 : KE_2) = 2:5}}$

Answer 2

Given : Two bodies of masses 2 kg and 5 kg respectively are moving at same velocity.

　

To find : What is the ratio of their kinetic energy.

　

Using formula :

★ KE = 1/2 mv².

　

Calculations :

→ KE = 1/2 mv²

→ KE 1/2 = 1/2 m1 v1/1/2 m2 v2

→ KE 1/2 = m1/m2

→ KE 1/2 = 2/5

→ KE = KE1 : KE2

→ KE 1 : KE 2 = 2 : 5

　

Therefore, the ratio of their kinetic energy will be 2:5.