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When the trolley shown in figure is given a horizontal acc a, the pendulum bob of mass m gets deflected to a max angle theta with the vertical. At the position of max deflection, show that the net acc of bob w.r.t trolley is gsin theta - a cos theta.

Ramesh V
70 Points
11 years ago

when the bob is maximum deflected, the radial component of acceleration due to its own weight, tries to restore the bob to original position, so the acceleration of bob inside trolley is : g sinx

the normal component of accln , g cosx will be equal to a.sinx at max. deflection

bob: ab = ( g.sinx i - g.cosx j )

in this directions of accln. of bob, the accln of trolley alone are taken, then tha acclns are shown in figure

trolley: at = ( a.cosx i + a.sinx j )

So, net accln. of bob w.r.t troley is anet = (g.sinx - a.cosx)

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Ramesh
IIT Kgp - 05 batch