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A ball of mass 1 kg is suspended by an inextensible string 1 m long attached to a point O of a smooth horizontal bar resting on fixed smooth supports A and B. The ball is released from rest from the position when the string makes an angle 30° with the vertical. The mass of the bar is 4 kg. The displacement of bar when ball reaches the other extreme position is

Asked by hariom2083 | 13 Oct, 2018, 09:30: AM
As shown in figure, let O be the centre of the rod of mass 4 kg.
Let us calculate the position of centre of mass (CM) of the system consists of rod of mass 4 kg and ball of mass 1 kg,
when the string connetcing the ball makes 30º vertical(right side). Point O is considered as origin of the coordinate system

x-coordinate of CM = [ 4×0+1×(1/2) ] / (4+1) = 0.1 m
y-coordinate of CM = [ 4×0+1×(√3/2) ] / (4+1) =  √3/10 m

When the ball moved to other extreme position (left side), coordinate of centre of mass will not change.

There will not be movement in vertical direction, hence no change in y-coordinate

x-coordintae of centre of the rod, when the ball moves to other extreme is calculted as follows

[ 4 × X +1×(-1/2) ] / (4+1) = 0.1 m ......................(1)

from (1) we get X = 0.25 m, Hence the bar will move 0.25m towards right side
Answered by Thiyagarajan K | 13 Oct, 2018, 08:06: PM
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