Question

Compare the momentum of 2 objects of mass 10kg and 40kg respectively but having same kinetic energy

Answer 1

P1 = root over 20 ×K.E
P2=root over 80×K.E
(Solutions is given as an image)

Answer 2

Given,

Mass of 2 objects is 10 kg and 40 kg, respectively.

To find,

The comparison of the momentum of both objects.

Solution,

We can simply solve this numerical problem by using the following process:

Let us consider that the first object has a mass M1 = 10 Kg and the second object has a mass M2 = 40 Kg, respectively.

Let us assume that the velocity of the Furst and second objects are V1 and V2, respectively.

Mathematically,

The momentum of an object = (mass)×(velocity)

The kinetic energy of an object= 1/2×(mass)×(velocity)^2

{Statement-1}

Now, according to the question;

The kinetic energy of the first object = kinetic energy of the second object

=> 1/2×(mass of the first object)×(velocity of the first object)^2 = 1/2×(mass of the second object)×(velocity of the second object)^2

{according to statement-1}

=> 1/2×(M1)×(V1)^2 = 1/2×(M2)×(V2)^2

=> {(M1)×(V1)}^2/(M1) = {(M2)×(V2)}^2/(M2)

=> (momentum of the first object)^2/(M1) = (momentum of the second object)^2/(M2)

{according to statement-1}

=> (momentum of the first object)^2/(momentum of the second object)^2 = (M1)/(M2) = (10 Kg)/(40 Kg) = 1/4 = (1/2)^2

=> (momentum of the first object)/(momentum of the second object) = 1/2

=> (momentum of the first object):(momentum of the second object) = 1:2

=> momentum of first object = 1/2×(momentum of the second object)

=> momentum of the first object is equal to half of the momentum of the second object

Hence, the momentum of the first object is equal to half of the momentum of the second object.