A body of mass $5 \,kg$ is moving with a momentum of $10\, kg-m/s$. A force of $0.2 \,N$ acts on it in the direction of motion of the body for $10\, seconds$. The increase in its kinetic energy is ............... $J$
A body of mass $5 \,kg$ is moving with a momentum of $10\, kg-m/s$. A force of $0.2 \,N$ acts on it in the direction of motion of the body for $10\, seconds$. The increase in its kinetic energy is ............... $J$
$2.8$
$3.2$
$3.8$
$4.4$
A body of mass $5 \,kg$ is moving with a momentum of $10\, kg-m/s$. A force of $0.2 \,N$ acts on it in the direction of motion of the body for $10\, seconds$. The increase in its kinetic energy is ............... $J$
Change in momentum = Force $×$ time
${P_2} - {P_1} = F \times t = 0.2 \times 10 = 2$
$⇒$ ${P_2} = 2 + {P_1} = 2 + 10 = 12kg{\rm{ - }}m/s$
Increase in K.E. = $\frac{1}{{2m}}(P_2^2 - P_1^2)\;$
$= \frac{1}{{2 \times 5}}\left[ {{{(12)}^2} - {{(10)}^2}} \right]$
$ = \frac{{44}}{{10}} = 4.4\,J$