Question

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity `v m//s`. If it is to climb the inclined surface then `v` should be :

A. `ge sqrt((10)/(7) gh)`
B. `ge sqrt(2gh)`
C. `2gh`
D. `(10)/(7) gh`

Answer 1

Correct Answer - A
`(K.E.)_(T) + (K.E.)_(R ) ge P.E`
`(1)/(2)mv^(2) + (1)/(2)I omega^(2) gemgh`
`(1)/(2)mv^(2) + (1)/(2) ((2)/(5)mr^(2)) omega^(2) ge mgh`
`(7)/(10)mv^(2) ge mgh`
`v ge sqrt((10 gh)/(7))`