Question #786a6

2 Answers
Dec 21, 2017

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

Dec 21, 2017

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 mentionedp_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.))