A block of mass `m = 1 kg` is released from point `A` along a smooth track as shown. Part `AB` is circular with radius `r_(1) = 4 m` and circular at `C` with radius `r_(2)`. Height of point `A` is `h_(1) = 2m` and of `c` is `h_(2) = 1m (g = 10 m//s^(2))`.
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The minimum safe value of `r_(2)` so that the block does not fly off the track at `C` is

Options

A. 1 m
B. 2 m
C. `1.5 m`
D. 3 m

Answer

B

Explanation

At `C N ge 0 (mv_(c)^(2))/(r_(2)) =mg`
`mgh_(1)=(1)/(2) mv_(c)^(2)+mgh_(2) , r_(2)=2(h_(1)-h_(2))`.