Momentum and force multiple choice

[lpettigrew]

Homework Statement

I found these questions and have attempted to solve them fully. Could anyone comment on my reasoning to substantiate my choices? I find I usually overlook details in mutiple choice questions and stumble to an answer. I was most uncertain about part i.

i. A body of mass 2 kg is travelling with twice the momentum of a body of mass 4 kg. What is the ratio of the kinetic energy of the first body to the kinetic energy of the second body?
A. 2:1
B. 1:2
C. 4:1
D. 8:1

ii. A body is moving in a circle at constant speed, and is being acted upon by several forces. Which of the following is true?
A. The resultant of all these forces balances the centripetal force.
B. The resultant of all these forces is the centripetal force making the body accelerate towards the centre.
C. The resultant of these forces balances the centrifugal force.
D.In addition to the forces acting there must be a centripetal force towards the centre.

iii. A rocket is ejecting 800 kg of hot gases every second and the gases are leaving at a speed of 500 m/s relative to the rocket. This causes a force on the rocket of:
A. 100 000 000 N
B. 1.6 N
C. 400 000 N
D. 50 000 000 N

Relevant Equations

KE=p^2/2m
F=p/t

i. Rearranging the equation for kinetic energy in terms of momentum;
1/2mv^2=(mv)^2/2m=p^2/2m
Inputting the values given KE=1^2/2*4kg = 1/8 J
Kinetic energy of a body with twice the momentum; KE=2^2/2*2kg =1 J

The ratio of the kinetic energy of the first body to the second body is therefore, 8:1, since 1J=8*1/8J. (option D)

ii. I believe that the resultant of all these forces is the centripetal force making the body accelerate towards the centre. (option B). For an object moving in a circle, this resultant force is the centripetal force that acts perpendicular to the direction of motion, towards the centre of the circle.

iii. Force=change in momentum/change in time
Force=(800*500)/1
Force = 400,000 N (option C)

 

[haruspex]

All good.