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CBSE Class 11-science Answered

A PARTICLE OF MASS M SLIDES DOWN A SMOOTH INCLINED PLANE OF ELEVATION theta FIXED IN AN ELEVATOR GOING UP WITH AN ACCELERATION A. FIND THE TIME TAKEN BY THE PARTICLE TO REACH THE BOTTOM IF THE BASE OF THE ELEVATOR HAS LENGTH L. 
Asked by ramkishoreagrawal50 | 10 Jan, 2016, 10:54: AM
answered-by-expert Expert Answer
Let us work in the elevator frame. A pseudo force ma0 in the downward direction is to be applied on the particle of mass m together with the real forces. 
Thus, the force on m,
(i) N normal force (ii) mg downward (by the Earth), (iii) ma0 downward (pseudo).
Let a be the acceleration of the particle with respect to the incline. 
Taking components of the forces parallel to the incline and applying Newton’s law, we get, 
mg sinθ + ma0 sinθ = m a 
or a = (g + a0) sinθ
This is the acceleration with respect to the elevator.
Now, cosθ = L/x, where x is the distance moved by the particle.
x = L/cosθ
From the equation of motion,
begin mathsize 14px style straight s equals ut plus 1 half at squared since comma space straight u equals 0 therefore straight s equals 1 half at squared end style
Hence,
begin mathsize 14px style straight L over cosθ equals 1 half left parenthesis straight g plus straight a subscript 0 right parenthesis sinθ space straight t squared straight t equals open parentheses fraction numerator 2 straight L over denominator left parenthesis straight g plus straight a subscript 0 right parenthesis sinθ cosθ end fraction close parentheses to the power of 1 divided by 2 end exponent end style
 
Answered by Faiza Lambe | 11 Jan, 2016, 01:08: PM

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