Work Energy and Power - Result Question 1
1. A force $F=20+10 y$ acts on a particle in $y$ direction where $F$ is in newton and $y$ in meter. Work done by this force to move the particle from $y=0$ to $y=1 m$ is :
[2019]
(a) $30 J$
(b) $5 J$
(c) $25 J$
(d) $20 J$
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Solution:
- (c) Work done by variable force
Work done, $W=\int _{y_i}^{y_f} F d y \Rightarrow \int _{y=0}^{y_f=1} F \cdot d y$
where, $F=20+10 y$
$ \begin{aligned} & \therefore \quad W=\int_0^{1}(20+10 y) d y \\ & =[20 y+\frac{10 y^{2}}{2}]_0^{1}=25 J \end{aligned} $
