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13.Oscillations
hard
જયારે બ્લોકને $2x_0$ દબાવીને મૂકત કરતા બ્લોકને દિવાલ સાથે અથડાતા કેટલો સમય લાગશે?
A
$ \frac{1}{6}\pi \sqrt {\frac{k}{m}} $
B
$ \sqrt {\frac{k}{m}} $
C
$ \frac{{2\pi }}{3}\sqrt {\frac{m}{k}} $
D
$ \frac{\pi }{4}\sqrt {\frac{k}{m}} $
Solution
(c)The total time from $A$ to $C$
${t_{Ac}} = {t_{AB}} + {t_{BC}}$
$ = (T/4) + {t_{BC}}$
where $T =$ time period of oscillation of spring mass system
${t_{BC}}$ can be obtained from, $BC = AB\sin (2\pi /T)\,{t_{BC}}$
Putting $\frac{{BC}}{{AB}} = \frac{1}{2}$ we obtain ${t_{BC}} = \frac{T}{{12}}$
==> ${t_{AC}} = \frac{T}{4} + \frac{T}{{12}} = \frac{{2\pi }}{3}\sqrt {\frac{m}{k}} $.
Standard 11
Physics
