Question

. A cat and dog are running with the same speed. If the weight of the dog is ten
times the cat, what is the ratio of their kinetic energies

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Answer 1

Given :

• Speed of cat = Speed of dog
• Weight of dof = 10×weight if cat

To find :

Ratio of kinetic energy

Formula used :

Kinetic energy [KE] = (1/2)mv²

Here,

• m = mass of body
• v = velocity of body

Let -

• Speed of cat = speed of dog = v
• Weight of cat = m

Solution :

weight of dog = 10× weight of cat

Weight of dog = 10m

KE of dog -

KE(dog) = (1/2) mass of dog × (speed of dog)²

KE(dog) = (1/2)×10m × (v)²

KE(dog) = 5mv²

KE of cat -

KE(cat) = (1/2)× mass of cat × (speed of cat)²

KE(cat) = (1/2) × m × (v)²

KE(cat) = (1/2)mv²

Ratio -

KE(dog) : KE(cat) = 5mv² : (1/2)mv²

KE(dog) : KE(cat) = 5 : (1/2)

KE(dog) : KE(cat) = 10 : 1

ANSWER :

KE(dog) : KE(cat) = 10 : 1

Additional points -

1. When speed of two objects are same, KE depends on mass only and is directly proportional.
2. When mass of two objects are same , KE is directly proportional to square of speed