Question

Two bodies whose masses are in ratio 1:2 , move with velocities 3v and v respectively . Find the ratio of their kinetic energies.​

Answer 1

☀️ Given that: Two bodies have their masses in ratio 1:2, and are moving with velocity 3v and v

     Need to find: Ratio of their kinetic energies

Understand that:

• We can let the masses of the bodies be m and 2m according to the given ratio.

• Formula of finding kinetic energy = mv²/2

Where,

m is mass of body

v is velocity of that body

Solution:

For Body 1-

• mass is 'm'
• velocity is '3v'

→ Kinetic energy = m × ( 3v )²/2

→ Kinetic energy = m × 9v²/2

→ Kinetic energy = 9mv²/2

For body 2-

• mass is '2m'
• velocity is 'v'

→ Kinetic energy = 2m × v²/2

→ Kinetic energy = 2mv²/2

Ratio of their kinetic energy -

→ 9mv²/2 : 2mv²/2

→ 9mv² : 2mv²

→ 9 : 2

⠀━━━━━━━━━━━━━━━━━━━  

• Henceforth, the ratio of their kinetic energies is 9:2

Answer 2

Answer:

Explanation:

kinetic energy, the form of energy that an object or particle has because of its motion. If work is done on an object that transfers energy through the action of a net force, the object accelerates and thus gains kinetic energy. The type of motion can be a translation (or movement along a path from one location to another), rotation about an axis, vibration, or any combination of motions.

If we want to accelerate an object, we must apply a force to it. Using power requires work from us. When the work is done, energy will be transferred to the object and the object will move at a new constant speed. The energy transferred is known as kinetic energy and depends on the mass and speed achieved.

Kinetic energy can be transferred between objects and transformed into other types of energy. For example, a flying squirrel may collide with a motionless chipmunk. After the collision, some of the squirrel's initial kinetic energy may have been transferred to the squirrel or converted into another form of energy.

Given that: Two bodies have masses in the ratio 1:2 and are moving at speeds of 3v and v

You need to find: The ratio of their kinetic energies

Understand it:

We can leave the masses of the bodies as m and 2m according to the given ratio.

The formula for finding kinetic energy = $mv^{2} /2$

Where,

m is the mass of the body

v is the velocity of this body

Solution:

For bodies 1-

mass is 'm'

speed is '3v'

→ Kinetic energy = $m*9v^{2} /2$/2

→ Kinetic energy = 9 $mv^{2} /2$

For the body 2-

weight is '2m'

speed is 'v'

→ Kinetic energy = $m*v^{2} /2$

The ratio of their kinetic energy -

→ 9$mv^{2} /2$ : 2$mv^{2}$/2

→ 9$mv^{2}$: 2$mv^{2}$

→ 9:2

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