Question

Two bodies have same velocities their kinetic energy are 30J and 250J find the ratio of their masses

Answer 1

$\boxed{\sf \green{Answer}}$

ratio of masses = 3:25

$\boxed{\sf \green{Explanation}}$

Given:

• velocities of two bodies are same

K.E. of

• 1st body = 30J
• 2nd body = 250J

To Find:

Ratio of the masses of the bodies

Solution:

w.k.t

$\boxed{\bold \blue{K.E = \dfrac{1}{2}m{v}^{2}}}$

$K.E_1= \dfrac{1}{2}m_1{v}^{2}$

$30J = \dfrac{1}{2}m_1{v}^{2}$ -----(1)

Now,

$K.E_2= \dfrac{1}{2}m_2{v}^{2}$

$250J= \dfrac{1}{2}m_2{v}^{2}$ ------(2)

Eq. (1)/(2)

$\dfrac{30J}{250J}= \dfrac{\dfrac{1}{2}m_1 {v}^{2}}{\dfrac{1}{2}m_2{v}^{2}}$

$\dfrac{3\cancel{0J}}{25\cancel{0J}}= \dfrac{\cancel{\dfrac{1}{2}}m_1 \cancel{{v}^{2}}}{\cancel{\dfrac{1}{2}}m_2\cancel{{v}^{2}}}$

$\dfrac{3}{25}= \dfrac{m_1 }{m_2}$

$m_1 : m_2 = 3 : 25$

$\texttt{\blue{Aravind}\:\red{Reddy}....!}$

Answer 2

★Given →

velocities of two bodies are same

velocities of two bodies are sameK.E. of

• 1st body = 30J
• 1st body = 30J2nd body = 250J

★To Find →

Ratio of the masses of the bodies

★Solution: →

$\boxed{\bold \orange{K.E = \dfrac{1}{2}m{v}^{2}}}$

$K.E_1= \dfrac{1}{2}m_1{v}^{2}$

$30J = \dfrac{1}{2}m_1{v}^{2}$

-----(1)

Now,

$K.E_2= \dfrac{1}{2}m_2{v}^{2}$

$250J= \dfrac{1}{2}m_2{v}^{2}$

------(2)

Eq. (1)/(2)

$\dfrac{30J}{250J}= \dfrac{\dfrac{1}{2}m_1 {v}^{2}}{\dfrac{1}{2}m_2{v}^{2}}$

$\dfrac{3\cancel{0J}}{25\cancel{0J}}= \dfrac{\cancel{\dfrac{1}{2}}m_1 \cancel{{v}^{2}}}{\cancel{\dfrac{1}{2}}m_2\cancel{{v}^{2}}}$

$\dfrac{3}{25}= \dfrac{m_1 }{m_2}$