Please explain each answer True or False. a) Two different particles that have t

Question

Please explain each answer

True or False.

a) Two different particles that have the same kinetic energy must also have the same momenta.

b) It is possible that a larger force may not produce a larger impulse on a body than a smaller force.

c)   It is possible to have a collision between 2 particles in which all of the initial kinetic energy possessed by the particles is "lost" after the collision.

d) The center of mass of a solid body could lie outside the body.

e)   The acceleration of the center of mass of 3 marbles thrown into the air simultaneously is -9.8 m/s2.

Explanation / Answer

part a:

let mass of one particle is m and other is 4*m.(can take any random value)

if the speed of the first particle is v1 and second particle is v2,

equating their kinetic energy:

0.5*m*v1^2=0.5*4*m*v2^2

==>v1=2*v2

momentum of first particle=m*v1=2*m*v2

momentum of second particle=4*m*v2

so they dont have the same momentum.

hence the statement is false.

part b:

impulse=force*time duration

so if larger force is applied for a small time duration, and smaller force is applied for large duration, then impulse applied by smaller force can be greater than that of larger force.

hence the statement is true.

part c:

consider anhilitation between positron and electron.

total energy is converted to heat energy.

so the statement is true.

part d:

if the body is irregular with gaps in between, center of mass can lie outside the body.

hence the statement is true.

part e:

if three marbles have mass m1,m2 and m3

each of them have acceleration -g.

where g=9.8 m/s^2

so acceleration of center of mass=-(m1*g+m2*g+m3*g)/(m1+m2+m3)=-g

hence the statement is true.

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