A particletiedto a stringof lengthl isdescribinga verticalcircleitsspeedat thebottommostpointis sqrt( 7gl ) .Thenitsspeedat thetopmostpointwillbe

A particletiedto a stringof lengthl isdescribinga verticalcircleitsspe

1.	A particletiedto a stringof lengthl isdescribinga verticalcircleitsspeedat thebottommostpointis sqrt( 7gl ) .Thenitsspeedat thetopmostpointwillbe
Answer» ` SQRT(gl)` ` sqrt(2GL)` ` sqrt( 3gl)` `sqrt( 5gl)` Solution :KINETICENERGYOF theparticleat thebottommostpoint`=(1)/(2) m ( sqrt( 7gl) ^(2))= (7) /(2) gl` The heightof theparticleis measuredfromthe bottom mostpointand itspotentialenergyat thispointcan bemostpointand itspotentialenergyat thispointcan betakento be`= mg* 0=0 ` ` therefore `totalenergyof theparticleat thebottommostpoint `=(7 )/(2)mg l + 0 =(7)/(2)m gl ` if thevelocityof theparticleat thetopmostpointis v . itskineticenrgy`=(1) /(2)MGL ` ifthevelocityof theparticleat thetopmostpointis ` V ,`itskineticenergy`=(1)/(2)m v^(2)` andpotentialenergy`= mgh = mg * 2l2mgl` `therefore ` TOTALENERGY`=((1)/(2) m v^(2) + 2mgl) ` so `(1)/(2) mv^(2)+ 2mgl= (7) /(2)mgl` or ` (1)/(2)mv^(2)= (3)/(2)mgl ` or`v= sqrt(3gl ) `