Work Power and Energy 5 Question 5
7. A particle is placed at the origin and a force $F=k x$ is acting on it (where, $k$ is a positive constant). If $U(0)=0$, the graph of $U(x)$ versus $x$ will be (where, $U$ is the potential energy function)
(2004, 2M) (a)
(c)
(b)
(d)
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Answer:
Correct Answer: 7. (a)
Solution:
- From $F=-\frac{d U}{d x}$
$$ \begin{aligned} & \int _0^{U(x)} d U=-\int _0^{x} F d x=-\int _0^{x}(k x) d x \\ \therefore \quad & U(x)=-\frac{k x^{2}}{2} \quad \text { as } U(0)=0 \end{aligned} $$
