Question

$\huge \sf \fbox\pink{question}$

A heavy truck and bike are moving with the same kinetic energy. if the mass of the truck is 4 times that of the bike, then calculate the ratio of their momenta.(Ratio of momenta = 2:1)

❥ Need a correct answer

❥ Step by step explaination needed

❥ Wrong answer will be reported ☺️​

Answer 1

Given: A heavy truck and bike are moving with the same kinetic energy. if the mass of the truck is 4 times that of the bike

To Find :

Ratio of their momentum ?

Solution:

As we have been provided that truck and bike are moving with same Kinetic Energy. And also mass of truck is 4 times that of bike .

For Bike :

Let the mass of bike be m

and , its velocity be v m/s

For Truck

The mass of truck will be 4m

and its velocity be v' m/s

Now, According to the Question

Kinetic Energy of Truck = Kinetic Energy of Bike

↠ 1/2×4m×v'² = 1/2×m×v²

↠ 4m × v'² = m ×v²

↠ 4m×v'²/m = v²

↠ 4v'² = v²

↠ v'² = v²/4

↠ v' = v/2 -------------(i)

Now, calculating the the ratio of their momentum .

• Momentum = mv

By using equation (i) we get

Momentum of Truck/Momentum of Bike = 4m×v/2/mv

Momentum of Truck/Momentum = 2mv/mv

Momentum of Truck/Momentum = 2/1

• Hence, the ratio of their momenta will be 2:1 .

Answer 2

Answer:

Question :-

✯ A heavy truck and bike are moving with the same kinetic energy. if the mass of the truck is 4 times that of the bike, then calculate the ratio of their momenta.

Given :-

✯ A heavy truck and bike are moving with the same kinetic energy. if the mass of the truck is 4 times that of the bike.

Find Out :-

✯ Calculate the ratio of their momenta.

Solution :-

◆ Let the mass of the Bike be m.

◆ Thus mass of the truck will be 4m.

☆ Let the velocity of the Bike be v

☆ Thus, the velocity of the truck be V.

Since, they are having the same kinetic energy.

According to the question or ATQ :&

➙ $\sf \dfrac{1}{2} mv^2 = \dfrac{1}{2} MV^2$

➙ $\sf mv^2 = 4mV^2$

➙ $\sf v^2 = (2V)^2$

➙ $\sf\boxed{\bold{v = 2V}}$

☣ For the Ratio of the Momentum,

$\red{ \boxed{\sf{\dfrac{Momentum of bike}{Momentum of car} = \dfrac{mv}{MV}}}}$

➙ $\sf \dfrac{m(2V)}{(4m)V}$

➙ $\sf 4 \times \dfrac{1}{2}$

➙ $\sf \dfrac{4}{2}$

➙ ${\small{\bold{\purple{\underline{2 : 1}}}}}$

Henceforth, theRatio of Momentum of truck to bike is 2 : 1 .

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