Two particles 1 and 2 are allowed to descend on two frictionless chords OP and OQ as shown in the figure. The ratio of the speeds of the particles 1 and 2, respectively when they reach the circumference is

Options

A. `1/2`
B. 2
C. `3/2`
D. `2/3`

Answer

A

Explanation

According to the question,

triangle made in a semicircle is right angle triangle,
In `DeltaOPQ`,
`rArr cos60^(@)=(OP)/(OQ) rArr OP = 2R times 1/2 rArr OP=R`
In `DeltaOPS`,
`rArr cos60^(@)=(OS)/(OP)`
`rArr OS=R(1/2)`
`rArr OS=R/2`
Velocity of the particle 1, `v_(1)=sqrt(2g(OS))=sqrt(gR)`
Velcoity of particle 2, `v_(2)=sqrt(2g(OQ))=2sqrt(gR)`
Hence, `v_(1)/v_(2)=sqrt(gR)/(2sqrt(gR))=1/2`