Question

A light and a heavy body have equal momentum, which one has greater kinetic energy

Answer 1

Answer:

momentum :- m1v1= m2v2 ..........(a)

Explanation:

now,,,,,

KEnergy = 1/2 m$v^{2}$

so....    KE ∝ Velocity

also from (a) :---- momentum = mv

momentum is equal which means

M ∝ 1/V

SO,,,

M↑ ∝ V↓ ∝ KE ↓ ( MOMENTUM = CONSTANT )

Answer 2

Light body will have greater kinetic energy

Explanation:

let the mass of lighter body = m₁

mass of heavier body = m₂

velocity of lighter body = v₁

velocity of heavier body = v₂

Linear momentum of any body is given as

$Momentum = Mass * velocity$

according to question momentum are equal

=> $P_{1} = P_{2}$

=> $m_{1}v_{1} = m_{2} v_{2}$         ........................................(1)

Kinetic energy of any body is the energy possessed by its motion and is given as

=>  $K.E. = \frac{1}{2} mv^{2}$

Kinetic energy of lighter body is  $K.E_{1} = \frac{1}{2} m_{1} v_{1} ^{2}$

=> $K.E_{1} = \frac{1}{2} m_{1} v_{1} ^{2}*\frac{m_{1} }{m_{1} }$              [multiply and divide by m₁]

=> $K.E_{1} = \frac{1}{2} P_{1} ^{2}*\frac{{1} }{m_{1} }$             ...............................(2)  

Similarly Kinetic energy of heavier body is given as

=> $K.E_{2} = \frac{1}{2} m_{2} v_{2} ^{2}$

=> $K.E_{2} = \frac{1}{2} m_{2} v_{2} ^{2}*\frac{m_{2} }{m_{2} }$              [multiply and divide by m₂ ]

=> $K.E_{2} = \frac{1}{2} P_{2} ^{2}*\frac{1 }{m_{2} }$          ..............................(3)

From equation (1),(2)and (3) we see the smaller is mass more will be its Kinetic energy and vice versa as in equation (1) momentum of both the bodies are equal

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