There is inclined surface of inclination `theta=30^(@)`. A smooth groove is cut into it forming angle `alpha` with AB. A steel ball is free to slide along the groove. If the ball is released from the point O at top end of the groove, the speed when it comes to A is `[g=10 m//s^(2)`]

Options

A. `sqrt(40) m//s`
B. `sqrt(20 ) m//s`
C. `sqrt(10) m//s`
D. `sqrt(15) m//s`

Answer

A

Explanation

length of groove `=sqrt(3^(2)+4^(2))=5m`
acceleration along the incline =`g sin theta =g sin 30^(@) g//2`
acceleration along the groove =`g//2 cos (90-alpha) =g//2 sin alpha=g/2xx4/5 =4 m//s^(2)`
`v^(4) =2as`
`v=sqrt(2xx4xx5) =sqrt(40) m//sec`