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5.Work, Energy, Power and Collision
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A particle of mass $m$ starts moving from origin along $x$-axis and its velocity varies with position $(x)$ as $v=k \sqrt{x}$. The work done by force acting on it during first " $t$ " seconds is ...........
A$\frac{m k^4 t^2}{4}$
B$\frac{m k^4 t^2}{8}$
C$\frac{m k^2 t}{2}$
D$\frac{m k^2 t^2}{4}$
Solution
(b)
$v=k \sqrt{x}$
Square both sides
$v^2=k^2 x \ldots (1)$
$v^2=(0)^2+2 a x \ldots (2)$
Compare $(1)$ and $(2)$
$2 a=k^2$
$a=\frac{k^2}{2}$
Displacement $x=\frac{1}{2} a t^2$
$=\frac{1}{2} \frac{k^2}{2} t^2$
$W = Fx$
$=\max$
$=\frac{m k^2}{2} \cdot \frac{1}{2} \frac{k^2}{2} t^2$
$=\frac{m k^4 t^2}{8}$
$v=k \sqrt{x}$
Square both sides
$v^2=k^2 x \ldots (1)$
$v^2=(0)^2+2 a x \ldots (2)$
Compare $(1)$ and $(2)$
$2 a=k^2$
$a=\frac{k^2}{2}$
Displacement $x=\frac{1}{2} a t^2$
$=\frac{1}{2} \frac{k^2}{2} t^2$
$W = Fx$
$=\max$
$=\frac{m k^2}{2} \cdot \frac{1}{2} \frac{k^2}{2} t^2$
$=\frac{m k^4 t^2}{8}$
Standard 11
Physics
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