Question

Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06p m and force constant 0.1 N/m. Initially, both the balls are displaced by angle q = p/6 radian with respect to the diameter PQ of the circle and released from rest. The frequency of oscillation of the ball B is –

• A. p Hz
• B. $\frac { 1 } { \pi }$Hz
• C. 2pHz
• D. 1/2p Hz

Answer 1

Answer: (B)

$\frac { 1 } { \pi }$Hz

Answer 2

µ = $\frac { 0.1 \times 0.1 } { 0.1 \times 0.1 }$ = $\frac { 0.1 } { 2 }$ ̃ k = k₁ + k₂ = 2 × 0.1