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) $20 J$

Show Answer

Solution:

  1. (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} $