A ball of mass 1 kg hangs in equilibrium from two strings O A and O B as shown in figure. What are the tensions in strings O A and O B ? (Take g=10 ms -2 )

Question

A ball of mass 1 kg hangs in equilibrium from two strings O A and O B as shown in figure. What are the tensions in strings O A and O B ? (Take g=10 ms -2 ) (A) 5 N, zero (B) Zero, N (C) 5 N , 5 √3 N (D) 5 √3 N , 5 N

Tardigrade Admin · Accepted Answer

Various forces acting on the ball are as shown in figure. The three concurrent forces are in equilibrium. Using Lami's theorem.

\frac{T _{1}}{s i n 15 0 ^{\circ}} = \frac{T _{2}}{s i n 12 0 ^{\circ}} = \frac{10}{s i n 9 0 ^{\circ}}

\frac{T _{1}}{s i n 3 0 ^{\circ}} = \frac{T _{2}}{s i n 6 0 ^{\circ}} = \frac{10}{1}

∴ T_{1} = 10 sin 3 0^{\circ}

= 10 \times 0.5 = 5 N

T_{2} = 10 sin 6 0^{\circ}

and

= 10 \times \frac{3}{2} = 53 N

Q. A ball of mass $1 k g$ hangs in equilibrium from two strings $O A$ and $OB$ as shown in figure. What are the tensions in strings $O A$ and $OB ?$ (Take $g = 10 m s^{- 2}$ )

5 N, zero

Zero, N

$5 N, 53 N$

$53 N, 5 N$

Q. A ball of mass 1kg hangs in equilibrium from two strings OA and OB as shown in figure. What are the tensions in strings OA and OB? (Take g=10ms−2 )

5 N, zero

Zero, N

5N,53​N

53​N,5N

Various forces acting on the ball are as shown in figure. The three concurrent forces are in equilibrium. Using Lami's theorem. sin150∘T1​​=sin120∘T2​​=sin90∘10​ sin30∘T1​​=sin60∘T2​​=110​ ∴T1​=10sin30∘ =10×0.5=5N T2​=10sin60∘ and=10×23​​=53​N

Q. A ball of mass $1 k g$ hangs in equilibrium from two strings $O A$ and $OB$ as shown in figure. What are the tensions in strings $O A$ and $OB ?$ (Take $g = 10 m s^{- 2}$ )

$5 N, 53 N$

$53 N, 5 N$