Keeping the velocity same, if the mass of the object is halved, find the ratio of new kinetic energy to the original kinetic energy.

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Solution

Kinetic energy is given by $K . E = \frac{1}{2} m v^{2}$
Original Kinetic energy, $K . E_{1} = \frac{1}{2} m_{1} v_{1}^{2}$
Changed Kinetic energy, $K . E_{2} = \frac{1}{2} m_{2} v_{2}^{2}$
Given, $m_{1} = 2 m_{2}$ and $v_{1} = v_{2}$
Thus, $\frac{K . E_{1}}{K . E_{2}} = \frac{m_{1}}{m_{2}} = \frac{2}{1} = 2 : 1$

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Keeping the velocity same, if the mass of the object is halved, find the ratio of new kinetic energy to the original kinetic energy.

Kinetic energy is given by K.E=12mv2 Original Kinetic energy, K.E1=12m1v21 Changed Kinetic energy, K.E2=12m2v22 Given, m1=2m2 and v1=v2 Thus, K.E1K.E2=m1m2=21=2:1