Question

If the mass of a body is doubled and its velocity becomes half,
then the linear momentum of the body will​ be?

Answer 1

Answer:

Kinetic energy of a body of given mass, is directly proportiional to its square of its velocity. When momentum is doubled, mass remaining constant, this means velcity is doubled. Hence, kinetic energy becomes 22=4 times i.e. say from 100 units to 400 units.

Answer 2

Answer :

• The linear momentum of the body is MV

Explanation :

Given :

• Mass of the body is doubled.
• Velocity of the body is halved.

To find :

• Linear momentum of the body.

Knowledge required :

Formula for momentum :

⠀⠀⠀⠀⠀⠀⠀⠀⠀p = mv

Where,

• m = Mass of the body
• p = Momentum
• v = Velocity

Solution :

Let the mass of the body be M and the velocity of the body be V.

When the mass of the body is doubled , mass is 2M and the when the velocity becomes half the velocity is V/2.

First let us find the momentum by the body without the change in mass and Velocity.

So by using the formula for momentum of a body and substituting the values in it, we get :

⠀⠀⠀⠀=> p = mv

⠀⠀⠀⠀=> p = ½ × M × V²

⠀⠀⠀⠀⠀⠀⠀∴ p = MV

Hence the momentum of the body is ½MV².

Now let's find out the momentum of the body when the mass is doubled and the velocity is halved.

⠀⠀⠀⠀=> p = mv

⠀⠀⠀⠀=> p = 2M × V/2

⠀⠀⠀⠀=> p = M × V

⠀⠀⠀⠀⠀⠀⠀∴ p' = MV

Hence the linear momentum of the body when mass is doubled and the velocity is halved is MV

Now to find the relationship between the linear momentum and original momentum of the body :

⠀⠀⠀⠀=> p" = p/p'

Now substituting the values in it, we get :

⠀⠀⠀⠀=> p/p' = MV/MV

⠀⠀⠀⠀=> p/p' = 1/1

⠀⠀⠀⠀=> p : p' = 1 : 1

Hence the relationships between the two momentum is 1 : 1.