Question

8. Two bodies which are equalin mass, move with uniform velocities of 6 ms and 18 ms, respectively.
Find the ratio of their kinetic energies.​

Answer 1

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

From the Question,

• Mass of both the bodies is equal

Let "u" and "v" be the velocities of both the bodies

• u = 6 m/s

• v = 18 m/s

Kinetic Energy of an object is given by:

$\huge{\boxed{\boxed{\sf{K = \frac{1}{2}m{v}^{2}}}}}$

Let k and K be the kinetic energies of the objects

Now,

$\sf{\frac{k}{K} = \frac{m{u}^{2}}{2}}{\frac{m{v}^{2}}{2}}$ $\sf{\because, the \ masses \ are \ equal}$ $\righttarrow \ \sf{\frac{k}{K} = \frac{{6}^{2}}{{18}^{2}}} \\ \\ \rightarrow \ \sf{\frac{k}{K} = \frac{36}{324}}$

$\huge{\rightarrow \ \mathtt{k : K = 1 : 9}}$

Thus,the ratio of their kinetic energies is 1 : 9

Answer 2

AnswEr :

⋆ Constant Mass of Both Body be x Kg.

$\bold{First \: Body} \begin{cases} \sf{Mass=x \: kg} \\ \sf{Velocity(v_1) =6m/s} \end{cases}$

$\bold{Second \: Body} \begin{cases} \sf{Mass=x \: kg} \\ \sf{Velocity(v_2)=18m/s} \end{cases}$

_________________________________

• We Know the Formula of Kinetic Energy :

$\boxed {\bf{Kinetic \: Energy = \dfrac{1}{2} \times Mass \times {Velocity}^{2} }}$

• Ratio of Kinetic Energies of Both Bodies :

$\longrightarrow \sf{K.E._1 : K.E._2}$

$\longrightarrow \sf{ \cancel{\dfrac{1}{2}m}{(v_1)}^{2} : \cancel{\dfrac{1}{2}m}(v_2) ^{2} }$

$\longrightarrow \sf{{(v_1)}^{2} : {(v_2)}^{2} }$

$\longrightarrow \sf{{(6)}^{2} : {(18)}^{2} }$

$\longrightarrow \sf{36 : 324}$

$\longrightarrow \large{\boxed{\sf{1: 9}}}$

⠀

$\therefore$ Ratio of Kinetic Energies will be 1 : 9.