Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is:
3:5
- 2:5
5:4
4:5
The Correct Option is B
Solution and Explanation
For objects with equal kinetic energies \(\left(\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}\right)\), we have:
\[\frac{p_1}{p_2} = \sqrt{\frac{m_1}{m_2}}\]
Substituting \(m_1 = 4 \, \text{g}\) and \(m_2 = 25 \, \text{g}\):
\[\frac{p_1}{p_2} = \sqrt{\frac{4}{25}} = \frac{2}{5}\]
Thus, the ratio of their momenta is 2 : 5.
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
