1.

A particle of mass `0.5kg` travels in a straight line with a velocity `v=(5x^(5//2))m//s`. How much work is done by the net force during the displacement from `x=0` to `x=2m` ?

Answer» Here,`m=0.5kg`
`v=5x^(5//2),W=?`
When `x=0,v_(1)=0`
When `x=2m, v_(2)=5(2)^(5//2)`
Using work energy theorem,
`W=` change in K.E. `=(1)/(2)mv_(2)^(2)-(1)/(2)mv_(1)^(2)`
`W=(1)/(2)m(v_(2)^(2)-v_(1)^(2))=(1)/(2)xx0.5[{5(2)^(5//2)}^(2)-0]`
`=(1)/(2)xx(1)/(2)xx25xx2^(5)=200J`


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