Two bodies of unequal masses have same Kinetic energy. Which one has greater linear momentum?

Solution

Given that, the kinetic energy of the two bodies is equal.
That is,
$space space space space space space space space space space 1 half space m subscript 1 v subscript 1 squared space equals space 1 half m subscript 2 v subscript 2 squared space rightwards double arrow space v subscript 2 squared over v subscript 1 squared space equals space m subscript 1 over m subscript 2 space rightwards double arrow v subscript 2 over v subscript 1 space equals space square root of m subscript 1 over m subscript 2 end root space$
Linear momentum is given by,
p₁ = m₁ v₁ and p₂ = m₂ v₂
Therefore, $space space space space space straight p subscript 2 over straight p subscript 1 space equals space fraction numerator m subscript 2 v subscript 2 over denominator m subscript 1 v subscript 1 end fraction space equals space m subscript 2 over m subscript 1. square root of m subscript 1 over m subscript 2 end root space equals space square root of m subscript 2 squared over m subscript 1 squared m subscript 1 over m subscript 2 end root space rightwards double arrow space straight p subscript 2 over straight p subscript 1 space equals space square root of m subscript 2 over m subscript 1 end root space$

That is mass has a direct dependence on linear momentum.
Hence, the heavier body will have a greater momentum.

Some More Questions From Work, Energy and Power Chapter

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

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Work, Energy And Power

Two bodies of unequal masses have same Kinetic energy. Which one has greater linear momentum?

Some More Questions From Work, Energy and Power Chapter

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

A man is rowing upstream and is at rest w.r.t. shore. Is he doing work w.r.t. shore?

Is frictional force conservative?

What is the work done by gravitational force in taking the mass m with constant velocity through height h?

A mass is tied with a string and whirled in horizontal circle. What is the work done by tension force?

Does the work done by force depend upon the velocity at that instant?

What is the work done by man against gravity when he is carrying a load on his head and walking on the horizontal road?

Are all central forces conservative?

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