Calculate Minimum Time of Sliding for Block on Wedge with Given Parameters

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mail_abhijit2006
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I RECENTLY GOT STUCK SOLVING THIS PROBLEM WHERE I WASN'T ABLE TO DIFFRENTIATE PROPERLY.THE PROBLEM GOES HERE BY.

Q. A BLOCK OF MASS m IS KEPT ON THE TOP OF THE WEDGE HAVING AN ANGLE OF INCLINATION a .THE FRICTION COEFFECIENT OF FRICTION BETWEEN THE BLOCK AND THE HYPOTENUSE OF THE WEDGE IS 'k'.THE LENGTH OF THE BASE OF THE ROD IS b . FOR WHAT VALUE OF ANGLE a WILL THE TIME OF SLIDING BE LEAST?
 
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