Question

the bodyof mass 4 kg and 25 kg has equal kinetic energy . The ratio of theri velocity will be​

Answer 1

Answer :

The ratio of their velocities = 5 : 2

Explanation :

Given,

• mass of a body, m₁ = 4 kg
• mass of another one, m₂ = 25 kg
• The two bodies have equal kinetic energy

To find,

• the ratio of their velocities

Solution,

Kinetic energy of an object is given by,

     $\sf \implies KE=\dfrac{1}{2}mv^2$

where

m is the mass of the object

v is the velocity of the object

Let

v₁ be the velocity of the first body of mass 4 kg

v₂ be the velocity of the second body of mass 25 kg

➙ KE of body of mass 4 kg,

  $\sf KE_1 =\dfrac{1}{2}m_1v_1^2 \\\\ KE_1=\dfrac{1}{2}(4 \ kg)(v_1^2) \\\\ KE_1=2v_1^2 \longrightarrow [1]$

 

➙ KE of body of mass 25 kg,

  $\sf KE_2=\dfrac{1}{2}m_2v_2^2 \\\\ KE_2=\dfrac{1}{2}(25 \ kg)(v_2^2) \\\\ KE_2=\dfrac{25}{2} v_2^2 \: \longrightarrow [2]$

Given,

KE₁ = KE₂

 $\sf 2v_1^2=\dfrac{25}{2}v_2^2 \\\\\\ 4v_1^2=25v_2^2 \\\\\\ \dfrac{v_1^2}{v_2^2} =\dfrac{25}{4} \\\\\\ \dfrac{v_1}{v_2}=\sqrt{\dfrac{25}{4}} \\\\\\ \dfrac{v_1}{v_2}=\sqrt{\dfrac{5^2}{2^2}} \\\\\\ \dfrac{v_1}{v_2}=\dfrac{5}{2}$

The ratio of their velocities = 5 : 2