Question

2. A heavy truck and bike are moving with
the same kinetic energy. If the mass of
the truck is four times that of the bike,
then calculate the ratio of their momenta,​

Answer 1

Answer:   1 : 2

Explanation:  We  have the relation between KE and momentum

                        KE = p^ 2/ 2m

For bike ; KE (1 ) = p^2 / 2m

mass of truck is four times the bike ,so  M = 4m ---(a) so,  

For truck ; KE (2) = p' ^2 / 2M

                            =  p'^2 / 8m   [from a]

Since there KE are same so,

KE(1) = KE(2)

p^2 / 2m = p' ^2 / 8m

Solving we get ,

p^2/p'^2 = 1/4

(p / p' ) ^2 = ( 1 / 2 )^ 2

p : p ' = 1 : 2  ans .

Answer 2

Given that a heavy truck and bike are moving with the same kinetic energy.

⇒ Kinetic energy of truck = Kinetic energy of bike

Also given that, the mass of the truck is four times that of the bike.

Let us assume that the mass of truck is 'm' and mass of bike is 'M'.

⇒ Mass of truck = 4 × mass of bike i.e. m = 4M ...........(1st equation)

We have to find the ratio of their mementa.

Now,

Relation between Kinetic energy and Momentum:

K = p²/2m

As kinetic energy of both truck and bike are equal. So,

→ p²/2m = (p')²/2M

→ p²/2(4M) = (p')²/2M

→ p²/8M = (p')²/2M

→ p²/4M = (p')²

→ p²/(p')² = 4/1

[ p = momentum of truck and p' = momentum of bike ]

→ (p/p')² = 4/1

→ p/p' = √(4/1)

→ p/p' = 2/1

Ratio of momentum of truck to bike is 2:1 and bike to truck is 1:2.