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A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions T₁ and T₂, respectively, are (in N) (Take acceleration due to gravity 10 m/s²)

Asked in JEE Main 2nd April 2nd Shift 2025 · Strings and ropes in equilibrium

Figure: Strings and ropes in equilibrium
Answer: (1) 5√3, 5

Step-by-step solution

Idea: the two strings are perpendicular to each other (60°+30°=90°), so the force triangle is right-angled and the tensions come out cleanly.

Let T₁ make 60° with the horizontal on the left and T₂ make 30° on the right.

Horizontal balance:

T₁ cos 60°=T₂ cos 30°

(T₁)/2=(√3)/2T₂, so T₁=√3 T₂.

Vertical balance:

T₁ sin 60°+T₂ sin 30°=mg=10

√3T₂·(√3)/2+T₂·1/2=10

(3T₂)/2+(T₂)/2=2T₂=10, so T₂=5 N and T₁=5√3 N.

Check: √T₁²+T₂²=√75+25=10 N, which is the weight — exactly what perpendicular strings must give.

Why the other options are wrong

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