Chapter 7, Problem 1OQ

You hold a slingshot at arm’s length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 200 cm/s. With the same procedure, you fire a bean with speed 600 cm/s. What is the ratio of the mass of the bean to the mass of the pebble? (a) $\frac{1}{9}$ (b) $\frac{1}{3}$ (c) 1 (d) 3 (e) 9

To determine

Ratio of masses.

Answer to Problem 1OQ

Option (A)

Explanation of Solution

Assume that light band of the sling shot puts equal amount of kinetic energy into the missiles.

Write down the equation for kinetic energy

  $E_1=\frac{1}{2}{m}_1{v}^2$        (I)

Here $E_1$ is the kinetic energy of bean, $m_1$ is the mass of bean and $v$ is the velocity

Equation (I) suggests that $E\propto v^2$

That is, when speed is increased 3 times, energy is increased to 9 times.

Write the expression for kinetic energy of the pebble.

  $E_2=\frac{1}{2}{m}_2\left(9v^2\right)$        (II)

Here $E_2$ is the kinetic energy of the pebble, $m_2$ is the mass of the pebble.

From (I) and (II),

  $\begin{array}{c}9E_1=E_2\\ 9\frac{1}{2}{m}_1{v}^2=\frac{1}{2}{m}_2{v}^2\\ \frac{m_1}{m_2}=\frac{1}{9}\end{array}$

Conclusion:

Option (A) is correct.