Question

Two objects of mass ratio 1:2 have ratio of kinetic energy A:1. If their momentum are same find A?

Answer 1

Given:-

→ Ratio of masses of the objects = 1 : 2

→ Ratio of kinetic energy = A : 1

→ Momentum of the objects are same.

To find:-

→ Value of 'A'.

Solution:-

Let the masses of the objects be 'm' and '2m' and kinetic energy of the objects be 'EA' [E×A] and 'A' respectively.

Since, momentum of the objects are same so we consider it as 'p'.

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Now, we know that :-

K.E. = p²/2m

For 1st object :-

⇒ EA = p²/2m. ----(1)

For 2nd object :-

⇒ E = p²/2(2m)

⇒ E = p²/4m. ----(2)

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On dividing eq.1 by eq.2, we get :-

⇒ EA/E = [p²/2m]/[p²/4m]

⇒ A = 4m/2m

⇒ A = 2

Thus, value of 'A' is 2 .

Answer 2

Answer:

Given :-

• Ratio of mass of two objects = 1:2
• Ratio of kinetic energy = A:1
• Mounmentum 1 = Mounmentum 2

To Find :-

A

Solution :-

We know that

KE = ½ mv²

So,

Since mass is 2 times more than 1st object so,

Let the masses be m and 2m

Now,

KE = p²/2m (1st object)

KE = p²/2 × 2m = p²/4m (2nd object)

On dividing,

⇒ EA/E = [p²/2m]/[p²/4m]

Cancelling E

⇒ A = [p²/2m]/[p²/4m]

Cancelling p²

⇒ A = 4m/2m

⇒ A = 4/2

⇒ A = 2

Value of 'A' is 2 .