Question

if the mass of a ball is increased 4 times from its original mass, then its kinetic energy will:
a remain the same
b decrease four times
c increase four times
d increase two times

Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity. Assume velocity \( v \) remains constant (since the problem doesn't mention a change in velocity).

Step2: Analyze Mass Change

Let the original mass be \( m_1 \) and new mass \( m_2 = 4m_1 \). Original KE: \( KE_1=\frac{1}{2}m_1v^2 \). New KE: \( KE_2=\frac{1}{2}(4m_1)v^2 = 4\times(\frac{1}{2}m_1v^2)=4KE_1 \). So KE increases 4 times.

Answer:

c. Increase four times