Question

Question #e3cb7

Answer 1

C) 1:2

Explanation:

First, find the velocities of both masses using the kinetic energy (KE) equation. Then, use the linear momentum (P) formula to find momentum for each of the masses. Lastly, find their ratio.

Formula for kinetic energy: `KE=1/2mv^2`

Formula for linear momentum: `P=mv`

1) Since both of the masses have equal kinetic energy, we can assume it to be any number to perform our calculations. Let's take the KE to be 8 Joules.

Now, using the KE formula, solve for `v` for both the given masses.

• For the 1g (0.001 kg) mass

`v=sqrt((2*KE)/m)=sqrt((2*8)/0.001)=126.491 ms^-1`

• For the 4g (0.004 kg) mass

`v=sqrt((2*KE)/m)=sqrt((2*8)/0.004)=63.246 ms^-1`

2) Now, use the values for velocity to find the momentum.

• For the 1g (0.001 kg) mass

`P_1= m*v=0.001*126.491=0.1265ms^-1`

• For the 4g (0.004 kg) mass

`P_2= m*v=0.004*63.246=0.2530ms^-1`

3) Finally, find their ratio.

Ratio of linear momentum of the 1g to 4g mass `= P_1/P_2`

`=0.1265/0.2530`

`=0.5`

`=1:2`

Answer 2

C.

Explanation:

Given are kinetic energies of two masses. We are required to find the ratio of their linear momenta.

Lets use Formula for kinetic energy in terms of linear momentum.

`KE=|vecp|^2/(2m)`

Now `KE_1=|vecp_1|^2/(2m_1) and KE_2=|vecp_2|^2/(2m_2)`

Using the given equality

`|vecp_1|^2/(2m_1)=|vecp_2|^2/(2m_2)`

Inserting values of respective masses we get

`|vecp_1|^2/(2xx1)=|vecp_2|^2/(2xx4)`
`=>|vecp_1|^2/|vecp_2|^2=1/4`
`=>|vecp_1|/|vecp_2|=1/2`