Chapter 5, Problem 2RAT

A $1-\text{kg}$ ball has the same speed as a $10-\text{kg}$ ball. Compared with $1-\text{kg}$ ball, the $10-\text{kg}$ ball has

(a) one-tenth the momentum

(b) the same momentum

(c) 10 times as much momentum

(d) 100 times as much momentum

To determine

The correct option for the statement “A $1-\text{kg}$ ball has the same speed as a $10-\text{kg}$ ball. Compared with $1-\text{kg}$ ball, the $10-\text{kg}$ ball has”.

Answer to Problem 2RAT

The correct option for the statement “A $1-\text{kg}$ ball has the same speed as a $10-\text{kg}$ ball. Compared with $1-\text{kg}$ ball, the $10-\text{kg}$ ball has” is option (c).

Explanation of Solution

Given info: The mass of the lighter ball is $1\text{kg}$, mass of the heavier ball is $10\text{kg}$ and speed of the both ball is $v$.

Write the expression to calculate the momentum of lighter ball.

$P_1=m_1\cdot v_1$

Here,

$P_1$ is the momentum of lighter ball

$m_1$ is the mass of the lighter ball

$v_1$ is the speed of the lighter ball

Write the expression to calculate the momentum of heavier ball.

$P_2=m_2\cdot v_2$

Here,

$P_2$ is the momentum ofheavier ball

$m_2$ is the mass of the heavier ball

$v_2$ is the speed of the heavier ball

Divide the expression for heavier ball by the expression for lighter ball.

$\frac{P_2}{P_1}=\frac{m_2\cdot v_2}{m_1\cdot v_1}$

Substitute $10\text{kg}$ for $m_2$, $1\text{kg}$ for $m_1$ and $v$ for $v_1$ and $v_2$ to find $P_2$.

$\begin{array}{c}\frac{P_2}{P_1}=\frac{\left(10\text{kg}\right)\left(v\right)}{\left(1\text{kg}\right)\left(v\right)}\\ \frac{P_2}{P_1}=10\\ P_2=10P_1\end{array}$

The momentum of the $10\text{kg}$ ball is 10 times the momentum of $1\text{kg}$ ball.

Conclusion:

Therefore, the correct option for the statement “A $1-\text{kg}$ ball has the same speed as a $10-\text{kg}$ ball. Compared with $1-\text{kg}$ ball, the $10-\text{kg}$ ball has ” is option (c).