Question

An object of mass 5kg moves with a velocity of 10m/s .........a)find the kinetic energy .......b)find the ratio between initial kinetic energy and final kinetic energy if:.....i) mass is doubled.......ii)velocity will be 3 times

Answer 1

Answer:

Mass = 5 kg

Velocity = 10 m/s

Kinetic Energy = 1/2 mv²

⇒ Kinetic Energy = 1/2 × 5 × 10 = 25 J

Now coming to the second part of the question.

Initial Kinetic Energy = 25 J

Final Kinetic Energy if mass is doubled = 1/2 × 10 × 10 = 50 J

⇒ Ratio = 25 J / 50 J = 1 / 2 or 1 : 2

Final Kinetic Energy if velocity is made 3 times = 1/2 × 5 × ( 30 )²

⇒ Final Kinetic Energy = 900 × 2.5 = 2250 J

⇒ Ratio = 25 / 2250 = 1 / 90 or 1 : 90

These are the required ratios.

Hope it helped !!

Answer 2

$\huge\bigstar\underline\mathfrak\pink{Explanation}$

Given :

Mass of object = 5 kg

Velocity of object = 10 m/s

We know that,

Kinetic energy = ½mv²

Put the given values in above formula,

Kinetic energy = ½ × 5 × 10 × 10

Kinetic energy = 250 J [ it will be Initial kinetic energy ]

Now,

Final kinetic energy if mass is doubled = ½×2m×v²

= ½ × 2 × 5 × 10 × 10

= 500 J

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Now,

Ratio between initial and final kinetic energy = 250 J : 500 J

= 1 : 2

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Also, we have to find final kinetic energy if velocity will be 3 times,

= ½ × m × (3v)²

= ½ × 5 × (3×10)²

= ½ × 5 × 900

= 2250 J

Ratio between initial and final kinetic energy = 25 : 2250

= 1 : 90

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