A particle suspended by a light inextensible thread of length l is projected horizontally from its lowest position with velocity `sqrt(7gl//2)`. The string will slack after swinging through an angle equal to

Options

A. `30^(@)`
B. `90^(@)`
C. `120^(@)`
D. `150^(@)`

Answer

C

Explanation

`h=l+l sintheta=l(1+sintheta)`

`v^(2)=u^(2)-2gh=u^(2)-2gl(1+sintheta)`
String will slack where, component of weight towards centre is just equal to centripetal force or,
`mgsintheta=(mv^(2))/(l)=(m)/(l)[u^(2)-2gl(1+sintheta)]`
Substituting `u^(2)=(7gl)/(2)`
we get, ` sintheta(1)/(2)` or `theta = 30^(@)`
`therefore` The desired angle is `90^(@)+30^(@)` or `120^(@)`