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Two particles having mass ratio n : 1 are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is
Asked by ekta.b | 09 Apr, 2022, 10:48: AM
answered-by-expert Expert Answer
Forces acting on mass m and mass ( n × m ) after releasing the system is shown in figure.
 
Heavy mass will move downwards and lighter mass mass move upwards. Magnitude of acceleration a is same for both masses
 
Magnitude of acceleration a = ( Net force ) / ( Total mass ) 
 
begin mathsize 14px style a space equals space fraction numerator left parenthesis n minus 1 right parenthesis m g over denominator left parenthesis n plus 1 right parenthesis m end fraction space equals space fraction numerator left parenthesis n minus 1 right parenthesis over denominator left parenthesis n plus 1 right parenthesis end fraction cross times g end style
Let us consider the coordinate system as shown in figure
 
acceleration of centre of mass acm is given as
 
begin mathsize 14px style a subscript c m end subscript space equals space fraction numerator left parenthesis n cross times m space right parenthesis cross times a space minus space m space cross times a over denominator left parenthesis n plus 1 right parenthesis space m end fraction space equals space fraction numerator left parenthesis n minus 1 right parenthesis over denominator left parenthesis n plus 1 right parenthesis end fraction cross times a space equals left parenthesis n minus 1 right parenthesis squared over left parenthesis n plus 1 right parenthesis squared cross times g space end style
Above acceleration of centre of mass is calculated with respect to origin of coordinated system considered.
Origin of coordinate system is centre of pulley .
Answered by Thiyagarajan K | 09 Apr, 2022, 12:30: PM
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