Question

(3) 0.45
Two particles 1 and 2 are allowed to descend on the
two frictionless chord OA and OB of vertical circle
at the same instant from point O. The ratio of the
velocities of the particles 1 and 2, when they reach
on the circumference will be (OB is diameter)
a
A
B.
sin a
(
(2) tan a
(3) cos a
(4) independent on a​

Answer 1

Answer:

Let radius of circle = R

Oq=Pq=R,   So △OPq is a equilateral triangle

So Particle on chord OP will travel vertical distance = Rcos60=  

2

R

​

 

∴ From work-energy theorem    mg(R/2)=  

2

1

​

mv  

1

2

​

⟹v  

1

​

=  

Rg

​

 

Particle on chord OQ will travel vertical distance  = 2R

Similarly for particle on OQ-      v  

2

​

=  

4Rg

​

=2  

Rg

​

 

Ratio of their speed =  

v  

2

​

 

v  

1

​

 

​

=  

2

1

​

Explanation: