Question

Two objects of masses 1 x 10-3 kg and 4 x 10-3 kg have equal momentum. what is the ratio of their kinetic energies?

Answer 1

Answer:

the ratio is 4:1

hope that helped u

Answer 2

Answer:

The ratio of their kinetic energies is 4:1

Explanation:

Given that,

The mass of objects are as follows

$m _{1} = 1 \times 10 {}^{ - 3} kg \\ m _{2} = 4 \times 10 {}^{ - 3} kg$

Also given that,they have equal momemtum.Tge relation for momentum is given as

$P=mv$

According to the given question,

$P _{1} =P _{2} = > m_{1}v_{1} = m_{2}v_{2} \\ = > \frac{v_{1}}{v_{2}} = \frac{m_{2}}{m_{1}} = \frac{4 \times 10 {}^{ - 3} }{1 \times 10 {}^{ - 3} } = 4$

The relation for kinetic energy is given as follows

$K.E = \frac{1}{2} mv {}^{2}$

Ratio is given as

$\frac{K.E _{1} }{K.E _{2}} = \frac{m _{1}v _{1} {}^{2} }{m _{2}v _{2} {}^{2} } = \frac{1 \times 10 {}^{ - 3} }{4 \times 10 {}^{ - 3} } \times (4) {}^{2} \\ = 4:1$

Therefore,the ratio of their kinetic energies is 4:1

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