A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving it a velocity of 7 m/s at the lowest point. Find the velocity at the highest point .

Explanation

Given :
mass of stone, `m=100gm=100xx10^(-3)kg`
length of string, `l=50cm=0.5m`
Velocity of mass in a vertical circle at lowest point,
`V_(L)=7m//sec`
Acceleration due to gravity.
`g=9.8m//sec^(2)`

According to law of conversation of energy,
Total energy at `L=` Total energy at `H`
`(K.E.)_(L)+(P.E.)_(L)=(K.E.)_(H)+(P.E.)_(H)`
At lowest point, `P.E.=0`
`K.E.=(1)/(2)mv_(L)^(2)`
At highest point, `P.E.=mg(2r)`
`K.E.=(1)/(2)mv_(H)^(2)`
Putting the values in equation `(i)`, we get
`(1)/(2)mv_(L)^(2)+0=(1)/(2)mv_(H)^(2)+mg(2r)`
`v_(L)^(2)=v_(H)^(2)+4gr`
`7^(2)=v_(H)^(2)+4xx9.8xx0.5`
`v_(H)^(2)=49-4xx4.9`
`v_(H)=5.422m//sec`.