Two identical balls A and B of mass m kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid pipe bent in the form of a circle as shown in figure. The pipe is fixed in a horizontal plane. The centers of the balls can move in a circle of radius r meter. Each spring has a natural length of r π π meter and spring constant K. Initially, both the balls are displaced by an angle 8 radian with respect to diameter PQ of the circles and released from rest. The speed of ball A when A and B are at the two ends of dia PQ is
Text Solution
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In stretched position of spring.
system P.E. = 2 × 
k × 2x 2 = 4kx 2
In mean position, both balls have kinetic energy only;
K.E. = 2 
but P.E. = K.E.
∴ ∴ 4Kx 2 = mv 2
or v = 2x 
= 2R θ θ 
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