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  • A ball of mass is dropped from a height <img alt="\mathrm{h= 10\, cm}" src="https:/

A ball of mass \mathrm{100\, g} is dropped from a height \mathrm{h= 10\, cm} on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance \mathrm{\frac{h}{2}}. The spring constant is ______ \mathrm{Nm^{-1}}.
\mathrm{\left ( Use\: g= 10 \; ms^{-2}\right )}

Option: 1

120


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer


Since the system is conservative ,
\mathrm{TE_{A}= TE_{C}}
\mathrm{mg\left ( h+\frac{h}{2} \right )+0= mg\left ( 0 \right )+\frac{1}{2}\, kx^{2}}

Compression in spring, \mathrm{x= \frac{h}{2}}
\mathrm{mg\times \left ( \frac{3h}{2} \right )= \frac{1}{2}k\left ( \frac{h^{2}}{4} \right )}
\mathrm{k= \frac{12\, mgh}{h^{2}}= \frac{12\, mg}{h}}
    \mathrm{= \frac{12\left ( 0.1 \right )\times 10}{\left ( 0.1 m\right )}}
\mathrm{k= 120\left ( N/m \right )}



 

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Riya

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