A force of $5 \mathrm{~N}$ acts on a body initially at rest. If the instantaneous power due to the force at…
A force of $5 \mathrm{~N}$ acts on a body initially at rest. If the instantaneous power due to the force at the end of the third second $(t=3 \mathrm{~s})$ is $5 \mathrm{~W}$, then the mass of the body is
$25 \mathrm{~kg}$
$12.5 \mathrm{~kg}$
$15 \mathrm{~kg}$
$7.5 \mathrm{~kg}$
Solution
Force acting on body, $F=5 \mathrm{~N}$
Instantaneous power, $P=5 \mathrm{~W}$
Acceleration in the body due to applying force $F$,
$
a=\frac{F}{m}=\frac{5}{m}
$
where, $m$ is mass of body
Velocity of body at $t=3 \mathrm{~s}$,
$
\begin{aligned}
& & v=0+a t=\frac{5}{m} \times 3 \\
& v & =\frac{15}{m}
\end{aligned}
$
Power, $P=F \times v$
$
\begin{array}{ll}
\Rightarrow & 5=5 \times \frac{15}{m} \\
\Rightarrow & m=15 \mathrm{~kg}
\end{array}
$