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A block slides down from top of a smooth inclined plane of elevation theta fixed in an elevator going up with an acceleration a_(0). The base of incline has length L. Find the time taken by the block to reach the bottom.

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :Let us solve the problem in the elevator frame. The free <a href="https://interviewquestions.tuteehub.com/tag/body-900196" style="font-weight:bold;" target="_blank" title="Click to know more about BODY">BODY</a> force diagram is <a href="https://interviewquestions.tuteehub.com/tag/shown-1206565" style="font-weight:bold;" target="_blank" title="Click to know more about SHOWN">SHOWN</a>. The forces are<br/><img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_NEO_CAO_PHY_XI_V01_MP1_C05_SLV_044_S01.png" width="80%"/><br/> (i) N normal reaction to the plane,<br/>(ii) <a href="https://interviewquestions.tuteehub.com/tag/mg-1095425" style="font-weight:bold;" target="_blank" title="Click to know more about MG">MG</a> acting vertically down,<br/>(iii) `ma_(0)` (pseudo force). acting vertically down <br/>If a is the acceleration of the body with respect to incline, taking components of forces<br/> parallel to the incline.<br/>`mg sin theta + ma_(0)sin theta = ma "" therefore "" a = (g+a_(0))sin theta`<br/>This is the acceleration with respect to the elevator <br/>The distance travelled is `(L)/(cos theta)`. If t is the time for reaching the <a href="https://interviewquestions.tuteehub.com/tag/bottom-401202" style="font-weight:bold;" target="_blank" title="Click to know more about BOTTOM">BOTTOM</a> of icline.<br/>`(L)/(cos theta)=0+(1)/(2)(g+a_(0))sin theta.t^(2)`<br/>`t=[(2L)/((g+a_(0))sin theta cos theta)]^((1)/(2))=[(4L)/((g+a_(0))sin 2 theta)]^((1)/(2))`</body></html>


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