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JEE Main 20254 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Morning Shift
Subject
Physics
Chapter
Laws of Motion

JEE Main 2025 · 4 April · Morning Shift · Physics · Laws of Motion

A body of mass m is suspended by two strings making angles θ_1 and...

A body of mass mm is suspended by two strings making angles θ1\theta_1 and θ2\theta_2 with the horizontal ceiling with tensions T1T_1 and T2T_2 simultaneously. T1T_1 and T2T_2 are related by T1=3T2T_1=\sqrt{3} T_2. the angles θ1\theta_1 and θ2\theta_2 are

Options

  1. Aθ1=30∘θ2=60∘\theta_1=30^{\circ} \theta_2=60^{\circ} with T2=3mg4\mathrm{T}_2=\frac{3 \mathrm{mg}}{4}
  2. Bθ1=60∘θ2=30∘\theta_1=60^{\circ} \theta_2=30^{\circ} with T2=mg2\mathrm{T}_2=\frac{\mathrm{mg}}{2}
  3. Cθ1=45∘θ2=45∘\theta_1=45^{\circ} \theta_2=45^{\circ} with T2=3mg4\mathrm{T}_2=\frac{3 \mathrm{mg}}{4}
  4. Dθ1=30∘θ2=60∘\theta_1=30^{\circ} \theta_2=60^{\circ} with T2=4mg5\mathrm{T}_2=\frac{4 \mathrm{mg}}{5}

Correct answer

B. θ1=60∘θ2=30∘\theta_1=60^{\circ} \theta_2=30^{\circ} with T2=mg2\mathrm{T}_2=\frac{\mathrm{mg}}{2}

Step-by-step solution

T1sin⁡θ1+T2sin⁡θ2=mgT1=3T2⇒T2[3sin⁡θ1+sin⁡θ2]=mg for  θ1=60∘θ2=30∘T2=mg2\begin{aligned} & \mathrm{T}_1 \sin \theta_1+\mathrm{T}_2 \sin \theta_2=\mathrm{mg} & \mathrm{ T}_1=\sqrt{3} \mathrm{ T}_2 \\ & \Rightarrow \mathrm{ T}_2\left[\sqrt{3} \sin \theta_1+\sin \theta_2\right]=\mathrm{mg} \\ & \text{\text{ for } } \theta_1=60^{\circ} & \theta_2=30^{\circ} \\ & \mathrm{T}_2=\frac{\mathrm{mg}}{2}\end{aligned}
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