1. Which one of the following statements is correct? A. If two objects have the

Question

1. Which one of the following statements is correct?

A. If two objects have the same momentum, they must have the same kinetic energy.

B. If two objects have the same momentum, the heavier one has the larger kinetic energy.

C. If two objects have the same momentum, the lighter one has the larger kinetic energy.

D. None of the previous.

2. You are standing on the edge of a dock, and jump straight down. If you land on sand, your stopping time is much shorter than if you land on water. If that is so, which one of the following statements is correct?

A. The sand exerts a larger impulse on you than does the water.

B. The sand exerts a smaller impulse on you than does the water.

C. The sand and the water exert the same impulse on you, but the sand exerts a greater average force.

D. The sand and the water exert the same impulse on you, but the sand exerts a smaller average force.

Explanation / Answer

(1) We know that momentum is = mass*Velocity
here m1V1 = m2V2
Now kinetic energy of 1 = (1/2)(m1V1)V1
Kinetic energy of 2 = (1/2)(m2V2)V2 = (1/2)(m1V1)V2
Now the one which have the lighter weight having the more velocity from the momentum equation .
Hence the lighter one having the more kinetic enegry

(2) We know that
impulse = Force*time
and Impulse = change in momentum
Since our momentum is going to zero in both cases therefore the applied impulse must be same in both cases.
But in the case of Sand , since the stopping time in sand is less than the water therefore the applied average force in the sand must be larger.
Hence correct option would be C.

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