contestada

The masses of two objects are 2 kg and 8 kg, respectively.If their kinetic energies are in 2:1 proportion, the ratio of their speeds is ___.
√2 :1
1:2
2√2 :1

Respuesta :

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{KE_1}{KE_2}=\dfrac{2}{1}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{0.5(2)v_1^2}{0.5(8v_2^2)}=\dfrac{2}{1}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{v_1^2}{4v_2^2}=\dfrac{2}{1}[/tex]

[tex]\\ \rm\Rrightarrow v_1^2=8v_2^2[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{v_1^2}{v_2^2}=\dfrac{8}{1}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{v_1}{v_2}=\dfrac{2\sqrt{2}}{1}[/tex]

[tex]\\ \rm\Rrightarrow v_1:v_2=2\sqrt{2}:1[/tex]

#BBH

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