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Question
A body of mass \(0. 5 ~ππ\) travels in a straight line with velocity \(π£ = ππ₯^{\dfrac{1}{2}}\) where \(π = 5 π^{\dfrac{1}{2}}S^{-1}\) . The work done by the net force during its displacement from to \(π₯ = 0\) \(π₯ = 2 π\) is
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Solution
Given,
Mass of the body,\((π) = 0. 5~ ππ\)
Velocity at any position \(π£ = ππ₯ ^{\dfrac{3}{2}}\)
Where \(π = 5 π^{-\dfrac{1}{2}}S^{-1}\)
From work-kinetic energy theorem
\(π = \Delta πΎ = πΎ_{π} β πΎ_{π}\)
\(π =\dfrac{1}{2} ππ£_ {π}^{2} β \dfrac{1}{2} ππ£_ {i}^{2}\)
\(π =\dfrac{1}{2} π (π£_{π}{2} β π£_{π}^{2}) \)
\(π = \dfrac{1}{2} \times0. 5\times\begin{Bmatrix}(5\times2^{\dfrac{3}{2}})^{2} β (5\times2^{\dfrac{3}{2}})^{2}\end{Bmatrix}\)
\(π = \dfrac{1}{2} \times0. 5\times200\)
\(π = 50 ~π½\)
Final Answer: (π)
Mass of the body,\((π) = 0. 5~ ππ\)
Velocity at any position \(π£ = ππ₯ ^{\dfrac{3}{2}}\)
Where \(π = 5 π^{-\dfrac{1}{2}}S^{-1}\)
From work-kinetic energy theorem
\(π = \Delta πΎ = πΎ_{π} β πΎ_{π}\)
\(π =\dfrac{1}{2} ππ£_ {π}^{2} β \dfrac{1}{2} ππ£_ {i}^{2}\)
\(π =\dfrac{1}{2} π (π£_{π}{2} β π£_{π}^{2}) \)
\(π = \dfrac{1}{2} \times0. 5\times\begin{Bmatrix}(5\times2^{\dfrac{3}{2}})^{2} β (5\times2^{\dfrac{3}{2}})^{2}\end{Bmatrix}\)
\(π = \dfrac{1}{2} \times0. 5\times200\)
\(π = 50 ~π½\)
Final Answer: (π)
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