A small bell starts moving from `A` over `a` fixed track as shown in the figure . Surface `AB` is friction from `A` to `B` the bell roll ralis without sipping `BC` is friction , `K_(A)K_(B)` and` K_(C)` are kinetic energy of the bell at `A, B` and `C` respacecvely.Then

Options

A. `h_(A) gt h_(C) , K_(B) gt k_(c)`
B. `h_(A) gt h_(C) , K_(c) gt k_(A)`
C. `h _(A) = h_(C) , K_(B) gt k_(c)`
D. `h_(A) lt h_(C) , K_(B) gt k_(c)`

Answer

A, B

Explanation

At point `A` , potential energy of the ball `= mgh_(A)`
At point `C` , potential energy of the ball `= mgh_(C)`
Total energy at point `A,E_(A) = K_(A) + mgh_(A)`
Total energy at point `B,E_(A) = K_(A) + mgh_(A)`
Total energy at point `C,E_(C) = K_(C) + mgh_(C)`
According to the law of conserveation of energy
`E_(A) = E_(B) = E_(C) ` ....(i)
E_(A) = E_(B) rArr E_(C)gt k_(C)` ....(ii)
E_(A) = E_(C)`
K_(A) + mgh_(A) = K_(B) + mgh_(C) ` ...(iii)
`rArr b_(A) gt b_(C) , K_(C) gt K_(A) ` ...(iv)
Option (b) is correct
force (i) (ii) and (iv) , we get h_(A) ,K_(B) gt K_(C)` Option (a) is correct .