Question

two bodies have masses in ratio 5:1 and kinetic energies in ratio 125:9 calculate the ratio of their velocities​

Answer 1

Answer:

5 : 3

Explanation:

 For small velocities kinetic energy is defined by half of the product of its mass and velocity^2.

  Here, bodies are defined by a and b.

Given,

$\implies\mathrm{\dfrac{K.E._a}{K.E._b} = \dfrac{\dfrac{1}{2}\times mass_a \times velocity_a ^2}{\dfrac{1}{2}\times mass_b \times velocity_b ^2}}\\\\\\\implies \mathrm{\dfrac{125}{9} =\dfrac{ mass_a \times velocity_a ^2}{mass_b \times velocity_b ^2}}\\\\\\\implies \mathrm{\dfrac{125}{9} =\dfrac{ 5\times velocity_a ^2}{1 \times velocity_b ^2}}\\\\\\\implies \mathrm{\dfrac{25}{9} =\dfrac{velocity_a ^2}{velocity_b ^2 }}\\\\\\\implies \mathrm{\dfrac{5}{3} =\dfrac{velocity_a}{velocity_b}}$

Answer 2

$\bigstar$ Solution :

$\bigstar$ Given :

• Two bodies have masses in ratio 5:1 and kinetic energies in ratio 125:9

$\bigstar$ To Find :

• The ratio of their velocities

$\bigstar$ Explanation :

• For small velocities kinetic energy is defined by half of the product of its mass and velocity². Here, bodies are defined by a and b. Given,

$\implies\mathrm{\dfrac{K.E._a}{K.E._b} = \dfrac{\dfrac{1}{2}\times mass_a \times velocity_a ^2}{\dfrac{1}{2}\times mass_b \times velocity_b ^2}}\\\\\\\implies \mathrm{\dfrac{125}{9} =\dfrac{ mass_a \times velocity_a ^2}{mass_b \times velocity_b ^2}}\\\\\\\implies \mathrm{\dfrac{125}{9} =\dfrac{ 5\times velocity_a ^2}{1 \times velocity_b ^2}}\\\\\\\implies \mathrm{\dfrac{25}{9} =\dfrac{velocity_a ^2}{velocity_b ^2 }}\\\\\\\implies \mathrm{\dfrac{5}{3} =\dfrac{velocity_a}{velocity_b}}$

$\star$ Therefore , Ratio of velocities is 5:3.

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