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A bob of mass `2kg` is suspended from point `O` of a core with an inextensible string strinng of length `sqrt(3)m`. It is moving in horizontal circle over the surface of cone as shown in the figure. Then `:(g=10m//s^(2))` A. bob looses contact with cone if`vgtsqrt(5)m//s`B. normal force on bob is `19N` when `v=2m//s`C. tension in string is `(38)/(sqrt(3))N` when `v=2m//s`D. normal force on bob is `(17)/(sqrt(3))N` when `v=2m//s` |
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Answer» Correct Answer - A::C `T=cos 30^(@)+N sin 30^(@)=mg` `rArr sqrt(3)T+N=2mg ......(i)` `T sin 30^(@)-N cos 30^(@)=(mv^(2))/((sqrt(3)//2))rArrT sin 30^(@)-3N =4mv^(2) .....(ii)` by `(i),(ii)= gt N =(2mg-4mv^(2))/(4) , T=(6mg-4mv^(2))/(4sqrt(3))` for `N gt 0rArr vlt sqrt(5) m//s` at `v=2, T=(38)/(sqrt(3))N , N=2N`. Solution `:` In `P,Q` and `S,` the centre of masses lies at `D//2` height from the base level. WHere as in `R(` cons `)` the complies at `D//4` height from the base. Hence `U_(P) gt U _(Q)` `Ans (C )`. |
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