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  • A trolley of mass 8kg as shown in figure, is connected to two identical springs, each

A trolley of mass 8kg as shown in figure, is connected to two identical springs, each of spring constant 400N/m. If the trolley is displaced from its equilibrium position by 9cm and released, the maximum speed of the trolley

Option: 1

0.9m/s


Option: 2

0.4m/s


Option: 3

0.3m/s


Option: 4

0.5m/s


Answers (1)

best_answer

\Delta E=0 \\

\Delta U S+\Delta K=0 \\

{\left[2\left(-\frac{1}{2} k x^2\right)+\left(\frac{1}{2} m v^2-0\right)\right]=0 } \\

-k x^2+\frac{1}{2} m v^2=0 \\

 \frac{1}{2} m v^2=k x^2 \\

 m v^2=2 k n^2 \\

 v^2=\frac{2 k x^2}{m}

 v=\sqrt{\frac{2kx^2}{m}} \\

 v=\sqrt{\frac{2 K}{m}} \times x                   

                   [\because k=400 \, \, \quad m=8kg \quad x=9cm]

v=\sqrt{\frac{2 \times 400}{8}} \times 9 \times 10^{-2}

 v=10 \times 9 \times 10^{-2} \\

 v=9 \times 10^{-1}

v=0.9 \mathrm{~m} / \mathrm{s}

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