Question

Two masses m and 2m at rest attains velocities 2v and v respectively on application force. Calculate the ratio of their kinetic energies.​

Answer 1

Answer:The ratio of the kinetic energies of the two masses is 2.

Explanation:

Answer 2

Answer:

2:1

Explanation:

To find the ratio of the kinetic energies of two masses 'm' and '2m' when they attain velocities '2v' and 'v' respectively, we use the formula for kinetic energy, which is:

$\boxed{ \left \begin{array}{ccc} \text{\underline{Kinetic Energy:}} \\\\ K = \dfrac{1}{2}mv^2 \\\\ \text{Where:} \\ \bullet \ K \ \text{is the kinetic energy} \\ \bullet \ m \ \text{is the mass of the object} \\ \bullet \ v \ \text{is the velocity of the object} \end{array} \right.}$

1. For the first mass 'm' with a velocity of '2v':

$\Longrightarrow K_1 = \dfrac{1}{2}(m)(2v)^2\\\\\\\\\Longrightarrow K_1 = \dfrac{1}{2}m(4v^2)\\\\\\\\\therefore K_1 = 2mv^2$

2. For the second mass '2m' with a velocity of 'v':

$\Longrightarrow K_2 = \dfrac{1}{2}(2m)(v)^2\\\\\\\\\Longrightarrow K_2 = \dfrac{1}{2}(2m)v^2\\\\\\\\\therefore K_2 = mv^2$

Now, the ratio of their kinetic energies K₁:K₂ is:

$\Longrightarrow \dfrac{2mv^2}{mv^2}\\\\\\\\\Longrightarrow \dfrac{2}{1}\\\\\\\\\therefore K_1:K_2=\boxed{2:1}$

Therefore, the ratio of their kinetic energies is 2:1.