Question

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

Answer 1

Let's see

`\\ \rm\Rrightarrow (KE_1)/(KE_2)=(2)/(1)`

`\\ \rm\Rrightarrow (0.5(2)v_1^2)/(0.5(8v_2^2))=(2)/(1)`

`\\ \rm\Rrightarrow (v_1^2)/(4v_2^2)=(2)/(1)`

`\\ \rm\Rrightarrow v_1^2=8v_2^2`

`\\ \rm\Rrightarrow (v_1^2)/(v_2^2)=(8)/(1)`

`\\ \rm\Rrightarrow (v_1)/(v_2)=(2√(2))/(1)`

`\\ \rm\Rrightarrow v_1:v_2=2√(2):1`

#BBH