A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be
- 1:1
- 2:1
- 1:4
- 4:1
The Correct Option is B
Solution and Explanation
The ratio of their respective momenta
⇒ \(\frac{P_1}{P_2}\) \(\bigg[P = \sqrt{ 2mKE}\bigg]\)
= \(\sqrt{ \frac{m_1}{m_2}}\)
= \(\sqrt{\frac{8}{2}} \; \; \; [mass = 8\;kg \;and\; 2\;kg]\)
= \(\frac{2}{1}\)
Therefore, the correct option is (B): \(\frac{2}{1}\)
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Concepts Used:
Gravitational Potential Energy
The work which a body needs to do, against the force of gravity, in order to bring that body into a particular space is called Gravitational potential energy. The stored is the result of the gravitational attraction of the Earth for the object. The GPE of the massive ball of a demolition machine depends on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between GPE and the mass of an object. More massive objects have greater GPE. Also, there is a direct relation between GPE and the height of an object. The higher that an object is elevated, the greater the GPE. The relationship is expressed in the following manner:
PEgrav = mass x g x height
PEgrav = m x g x h
Where,
m is the mass of the object,
h is the height of the object
g is the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.