Question

Question #786a6

Answer 1

The ratio of their `KE` is `=3/2`

Explanation:

The momentum is `P=mv`

The masses are `m_1=10kg` and `m_2=15kg`

As their momentum are identical

`p=m_1v_1=m_2v_2`

So,

`10*v_1=15*v_2`

`v_2=10/15v_1=2/3v_1`

Therefore,

Their kinetic energies are

`KE_1=1/2m_1v_1^2=1/2*10*v_1^2=5v_1^2`

`KE_2=1/2m_2v_2^2=1/2*15*v_2^2=15/2*(2/3v_1)^2`

`=15/2*4/9*v_1^2=10/3v_1^2`

Therefore,

`((KE_1)/(KE_2))=(5v_1^2)/(10/3v_1^2)=3/2`

Answer 2

The first objects KE is `3/2` times more than the second objects KE.

Explanation:

We know that,

Momentum,`color(blue)(p=mv`

The mass of the first object,`m_1=10 kg`

The mass of the second object,`m_2=15kg`

`:.`The momentum of the first object`,p_1=m_1v_1=10v_1`

`:.`the momentum of the second object`,p_2=m_2v_2=15v_2`
As,you mentioned`p_1=p_2`
Hence,`m_1v_1=m_2v_2`
`or,10v_1=15v_2`

`:.v_1/v_2=15/10=3/2`[As it is a ratio, there will remain no unit.]
We know,
`color(green)(kE=1/2(mv^2))`
Then,`(KE_1)/(KE_2)=(cancel(1/2)m_1v_1^2)/(cancel(1/2)m_2v_2^2)=m_1/(m_2).(v_1/v_2)^2=(10cancel(kg))/(15cancel(kg)).(3/2)^2=2/3.(9/4)=3/2color(brown)((Ans.))`