Question

two bodies of mass 2 gram and 4 gram having same kinetic energy having the ratio of their linear momentum​

Answer 1

Answer:

Ratio of their Linear Momentum = ✓2 / 2

Explanation:

Let the mass and velocity of 1st body be m1 and v1

Let the mass and velocity of 2nd body be m2 and v2 .

Given , kinetic energy is same :

Hence ,

( 1 / 2 ) * m1 * ( v1 )² = ( 1 / 2 ) * m2 * ( v2 )²

Given , m1 = 2grams and m2 = 4 grams

Hence , ( v1 )² = 2( v2 )²

=) ( v1 )² / ( v2 )² = 2 / 1

=) v1 / v2 = ✓2 / 1 — Equation ( 1 )

Now , ratio of their Linear momentum is :

=) ( m1 * v1 ) / ( m2 * v2 ) = 2 * V1 / 4* v2

=) v1 / ( 2 *v2 ) = ( 1 / 2 ) * v1 / v2

=) ( 1 / 2 ) * ✓2 ( substituting value of v1 / v2 from equation 1 )

=) ✓2 / 2

Answer 2

Concept:

• Momentum and kinetic energy

Given:

• m1 = 2 g
• m2 = 4 g
• Both m1 and m2 have the same kinetic energy

Find:

• The ratio of linear momenta of both bodies

Solution:

KE = 1/2mv^2

This equation can be re-written as

KE = (m^2v^2)/2m

KE = (mv)^2/2m

Linear momentum is the product of mass and velocity

p = mv

KE = p^2/2m

Since both kinetic energies are the same,

p1^2/2m1 = p2^2/2m2

p1^2/2 = p2^2/4

p1^2 = p2^2/2

p1^2/p2^2 = 1/2

p1/p2 = 1/√2

The ratio of their linear momenta is 1/√2

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