A body of mass $4 \mathrm{~kg}$ is moving with momentum of $8 \mathrm{~kg} \mathrm{~ms}^{-1}$. A force of $0…
A body of mass $4 \mathrm{~kg}$ is moving with momentum of $8 \mathrm{~kg} \mathrm{~ms}^{-1}$. A force of $0.2 \mathrm{~N}$ acts on it in the direction of motion of the body for 10 seconds. The increase in kinetic energy in joules is
$10$
$8.5$
$4.5$
$4$
Solution
$
\begin{aligned}
m & =4 \mathrm{~kg}, p=8 \mathrm{~kg} \mathrm{~m} / \mathrm{s} \\
F & =0.2 \mathrm{~N}, t=10 \mathrm{sec}
\end{aligned}
$
From Newton's IInd law
Force $=$ rate of change of momentum
$
\begin{aligned}
& F=\frac{p_2-p_1}{t} \\
& 0.2=\frac{m v-8}{10} \\
& 2=4 \times v-8 \\
& 4 v=10 \\
& \Rightarrow \quad v=\frac{5}{2} \mathrm{~m} / \mathrm{s} \\
& \therefore \quad \text { Final momentum } p_2=m v=4 \times \frac{5}{2} \\
& =10 \mathrm{~kg} \mathrm{~m} / \mathrm{s} \\
&
\end{aligned}
$