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 sin`theta `=l(1+sin`theta`)
`v^2=u^2-2gh=u^22gl(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)]`
On substituting `u^2=(7gl)/(2)`
`we get ,sin theta=(1)/(2)or theta=30^@`
`therefore " "the desired angle is " (90^@+30^@)or120^@`