Question

the kinetic energy of a moving object changes from $k_0$ to $4k_0$. by what factor does the magnitude of the object’s momentum change?
a 1
b 2
c 4
d 10

Explanation:

Step1: Write the kinetic energy formula

The kinetic energy formula is \(K = \frac{p^{2}}{2m}\), where \(p\) is momentum and \(m\) is mass. So, \(p=\sqrt{2mK}\).

Step2: Find the initial and final momentum

Initially, \(p_{0}=\sqrt{2mK_{0}}\). Finally, \(p_{f}=\sqrt{2m\times4K_{0}}=\sqrt{8mK_{0}}\).

Step3: Calculate the factor

Divide \(p_{f}\) by \(p_{0}\): \(\frac{p_{f}}{p_{0}}=\frac{\sqrt{8mK_{0}}}{\sqrt{2mK_{0}}}=\sqrt{\frac{8mK_{0}}{2mK_{0}}}=\sqrt{4} = 2\).

Answer:

B. 2