Question

Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 1515 grams and velocity of 77 centimeters per second has a kinetic energy of 147147 ergs. Find the kinetic energy for a mass of 1010 grams and velocity of 99 centimeters per second?

Answer 1

Answer:

The second kinetic energy is 162 J.

Explanation:

Given that,

Mass, $m_1=15\ g$

Velocity, $v_1=7\ cm/s$

Kinetic energy, $K_1=147\ ergs$

Mass, $m_2=10\ g$

Velocity, $v_2=9\ cm/s$

We need to find kinetic energy $K_2$. Kinetic energy is given by :

$K=\dfrac{1}{2}mv^2$

So,

$\dfrac{K_1}{K_2}=\dfrac{m_1}{m_2}\times \dfrac{v_1^2}{v_2^2}\\\\K_2=\dfrac{K_1}{\dfrac{m_1}{m_2}\times \dfrac{v_1^2}{v_2^2}}\\\\K_2=\dfrac{147}{\dfrac{15}{10}\times \dfrac{7^2}{9^2}}\\\\K_2=162\ J$

So, the second kinetic energy is 162 J.