Question

The momentum of a bullet of mass \[20\,g\] fired from the gun is \[10\,kg\dfrac{m}{s}\] .The kinetic energy of the bullet in \[kJ\] will be:
A. \[5\]
B. \[1.5\]
C. \[2.5\]
D. \[25\]

Answer 1

Hint:In the question they gave us momentum and asked to find kinetic energy so we wrote a kinetic energy formula in terms of momentum and mass of body. Then as the mass of the body was given in grams it was converted to kilograms and kinetic energy was computed.

Formula used:
The formula for kinetic energy is,
\[K.E = \dfrac{{{p^2}}}{{2m}}\]
where \[p\] is momentum and \[m\] is mass of the body.

Complete step by step answer:
The mass of the body is \[20\,g\] or \[0.02\,kg\] as \[1\,kg = 1000\,g\].
The momentum is given as \[10\,kg\dfrac{m}{s}\].
Therefore we have the formula kinetic energy,
\[K.E = \dfrac{{{p^2}}}{{2m}}\]
where \[p\] is momentum and \[m\] is mass of body.

Now we substitute the given values in the above formula as follows: taking values of momentum and mass which was given in grams convert it to kilograms as momentum was given in \[kg\dfrac{m}{s}\].
\[K.E = \dfrac{{{{10}^2}}}{{2 \times 0.02}}\]
\[ \Rightarrow K.E = 2500J \\
\therefore K.E= 2.5\,kJ\]

Therefore the correct answer is option C.

Note:Students often confuse directly taking the given values in the formula so take values in the same units both for numerator and denominator (here as in kinetic energy formula). So as the mass was given in grams and momentum was given in terms of kilograms convert mass into kilograms and compute the kinetic energy.