A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles 30^ and 60^ from vertical (lowest positions) are T₁ and T₂ , respectively. Then

Step-by-step solution

Tension, ( T = mv ^2 r + mg ) For ( =30^ ) ( aligned & T ₁= mv ^2 r + mg 30^ & = mv ^2 r + 3 2 mg aligned ) For ( =60^ ) ( aligned & T ₂= mv ^2 r + mgcos ^ 60^ & mv ^2 r + 1 2 mg & ~T ₁ > T ₂ aligned )