the linear momentum of a body of mass m is p then its kinetic energy will be
The linear momentum of a body of mass m is p then its kinetic energy will be
Answer:
The linear momentum of a body with mass ( m ) is given as ( p ). The linear momentum ( p ) is related to the velocity ( v ) of the body by the equation ( p = m \cdot v ).
The kinetic energy (( KE )) of an object is given by the formula KE = \frac{1}{2} m v^2 , where ( m ) is the mass of the object and ( v ) is its velocity.
Given that the linear momentum is ( p ) and mass is ( m ), we can express the velocity ( v ) in terms of ( p ) and ( m ):
p = m \cdot v
v = \frac{p}{m}
Now, substituting this velocity into the kinetic energy formula, we get:
KE = \frac{1}{2} m \left( \frac{p}{m} \right)^2 = \frac{1}{2} \cdot \frac{p^2}{m}
Therefore, the kinetic energy of the body with linear momentum ( p ) and mass ( m ) is \frac{p^2}{2m}