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Question

Two particles move parallel to x-axis about the origin with same amplitude ‘a’ and frequency ω. At a certain instant they are found at a distance a/3 from the origin on opposite sides but their velocities are in the same direction. The phase difference between the two particles is..

A
cos179
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B
cos159
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C
cos149
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D
cos119
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Solution

The correct option is A cos179
Letx1=asinωtand x2=asin(ωt+δ)betwoS.H.Ma3=asinωtand a3=asin(ωt+δ)sinωt=13andsin(ωt+δ)=13Eliminatingt,13cosδ+119sinδ=139cos2δ+2cosδ7=0cosδ=1or78i.e.,δ=180orcos1(79)Nowv1=aωcosωtandv2=aωcos(ωt+δ)Ifweputδ=180Wefindthatv1andv2areofoppositesigns.Henceδ=180isnotapplicable.δ=cos179

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