Question

a) Two objects of masses 3 kg and 6 kg are moving with the same

momentum of 30 kgms​-1.

(i) Will they have the same kinetic energy?

(ii) Will they have the same speed? Prove it.

​

Answer 1

Explanation:

Given:

• Mass of two objects (m) = 3 kg and 6 kg
• Momentum of both objects (P) = 30 kg m/s

To find:

• Will they have same kinetic energy (K.E) = ?
• Will they have same speed = ?

Solution:

Let's first find the velocities of both objects.

Let the two objects be A and B.

We know, $\pink{\sf{Momentum\:=\:m\:\times\:v.}}$ Here, we know the momentum and mass so we'll find the velocities of both objects one by one.

$\longrightarrow\:\sf{30\:=\:3\:\times\:v_A}$

$\longrightarrow\:\sf{\dfrac{30}{3}\:=\:v_A}$

Velocity of object A is 10 m/s.

$\longrightarrow\:\sf{30\:=\:6\:\times\:v_B}$

$\longrightarrow\:\sf{\dfrac{30}{6}\:=\:v_B}$

Velocity of object B is 5 m/s.

(i) No, tey will not have the same kinetic energy. Let's prove it !

We remember, $\green{\sf{Kinetic\:energy\:=\:\dfrac{1}{2}mv^2}}$

Find the K.E for both objects.

$\longmapsto\:\sf{K.E_A\:=\:\dfrac{1}{2}\:\times\:3\:\times\:(10)^2}$

$\longmapsto\:\sf{K.E_A\:=\:\dfrac{1}{2}\:\times\:3\:\times\:100}$

$\longmapsto\:\sf{K.E_A\:=\:3\:\times\:50}$

$\therefore$ Kinetic energy of object A is 150 J.

$\longmapsto\:\sf{K.E_B\:=\:\dfrac{1}{2}\:\times\:6\:\times\:(5)^2}$

$\longmapsto\:\sf{K.E_B}$ = 3 × 25

$\longmapsto\:\sf{K.E_B}$ = 75

$\therefore$ Kinetic energy of object B is 75 J.

Hence, proved that kinetic energies of both the objects is not same.

(ii) No, their speeds will also nit be same. We have proved above that A has the velocity of 10 m/s and B has the velocity of 5 m/s.

Answer 2

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

I) no

ii) no

$\red{\mid{\underline{\overline{\textbf{Explanation}}}\mid}}$

It is given that :-

Mass of first object = 3kg

Mass of second object = 6kg.

Momentum of both bodies = 30kgm/s

Kinetic energy= ?

Velocity = ?

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i ) Momentum of a body is the product of its mass and velocity. It is represented by the expression :

$\red{\mid{\underline{\overline{\textbf{p = mv}}}\mid}}$

Where :

• P = Momentum
• m = mass of body
• v = velocity of body.

Now for the first body,its momentum is 30kgm/s and mass is 3 kg. After inputting these values in equation we get :

$30 = 3 \times v$

$v = \frac{30}{3} = 10$

Therefore we got that velocity of first body is 10m/s.

$V_b1 = 10m/s$

Now, it's also given mass of second body to be 6kg and the momentum is 30kgm/s.

So again inputting the known values for second body we get :

$30 = 6 \times v \\ \\ v = \frac{30}{6} = 5m/s$

Thus we got that final velocity of second body is 5m/s.

Now. kinetic energy of a body is determined ad the energy of a body due to it's motion. It is half of product of mass and square of velocity of a body. We can define it by the expression :

$k = \frac{1}{2} \times m {v}^{2}$

Now after inputting the known values in this equation we get , kinetic energy of first body to be :

$k = \frac{1}{2} \times 3 \times {10}^{2} \\ k = \frac{1}{2} \times 3 \times 100 = 50 \times 3 =150$

Therefore kinetic energy of First body is 150joule.

$K_a = 150j$

And similarly doing for second body we get :

$k = \frac{1}{2} \times 6 \times {5}^{2} = 3 \times 25 = 75$

Therefore kinetic energy of second body is 75J

$K_b = 75j$

Now we can see that :

$K_a > K_b$

Thus kinetic energy of both bodies is not same.

ii) And it has been calculated that there velocities are different. .

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BY SCIVIBHANSHU

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