A body of mass m is suspended by two strings making angles and with he horizontal ceiling with tensions and simultaneously. and are related by the angle and are [2025]

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Q.
A body of mass m is suspended by two strings making angles $θ_{1}$ and $θ_{2}$ with the horizontal ceiling with tensions $T_{1}$ and $T_{2}$ simultaneously. $T_{1}$ and $T_{2}$ are related by $T_{1} = \sqrt{3} T_{2}$ . The angle $θ_{1}$ and $θ_{2}$ are [2025]

1 $θ_{1} = 30 °, θ_{2} = 60 ° with T_{2} = \frac{3 m g}{4}$

2 $θ_{1} = 60 °, θ_{2} = 30 ° with T_{2} = \frac{m g}{2}$

3 $θ_{1} = 45 °, θ_{2} = 45 ° with T_{2} = \frac{3 m g}{4}$

4 $θ_{1} = 30 °, θ_{2} = 60 ° with T_{2} = \frac{4 m g}{5}$

Ans.
(2)

$T_{1} \sin θ_{1} + T_{2} \sin θ_{2} = m g$

$T_{1} \cos θ_{1} = T_{2} \cos θ_{2}$

$\sqrt{3} T_{2} \cos θ_{1} = T_{2} \cos θ_{2}$

$\sqrt{3} \cos θ_{1} = \cos θ_{2}$

For $θ_{1} = 60 °, θ_{2} = 30 °$

$\sqrt{3} T_{2} \cdot \frac{\sqrt{3}}{2} + T_{2} \cdot \frac{1}{2} = m g \Rightarrow T_{2} = \frac{m g}{2}$

Solution

Q.
A body of mass m is suspended by two strings making angles $θ_{1}$ and $θ_{2}$ with the horizontal ceiling with tensions $T_{1}$ and $T_{2}$ simultaneously. $T_{1}$ and $T_{2}$ are related by $T_{1} = \sqrt{3} T_{2}$ . The angle $θ_{1}$ and $θ_{2}$ are [2025]

1 $θ_{1} = 30 °, θ_{2} = 60 ° with T_{2} = \frac{3 m g}{4}$

2 $θ_{1} = 60 °, θ_{2} = 30 ° with T_{2} = \frac{m g}{2}$

3 $θ_{1} = 45 °, θ_{2} = 45 ° with T_{2} = \frac{3 m g}{4}$

4 $θ_{1} = 30 °, θ_{2} = 60 ° with T_{2} = \frac{4 m g}{5}$

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Solution

Q. A body of mass m is suspended by two strings making angles θ1 and θ2 with the horizontal ceiling with tensions T1 and T2 simultaneously. T1 and T2 are related by T1=3T2. The angle θ1 and θ2 are [2025]

1 θ1=30°, θ2=60° with T2=3mg4

2 θ1=60°, θ2=30° with T2=mg2

3 θ1=45°, θ2=45° with T2=3mg4

4 θ1=30°, θ2=60° with T2=4mg5

Ans. (2) T1sinθ1+T2sinθ2=mg T1cosθ1=T2cosθ2 3T2cosθ1=T2cosθ2 3cosθ1=cosθ2 For θ1=60°, θ2=30° 3T2·32+T2·12=mg ⇒T2=mg2

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Q.
A body of mass m is suspended by two strings making angles $θ_{1}$ and $θ_{2}$ with the horizontal ceiling with tensions $T_{1}$ and $T_{2}$ simultaneously. $T_{1}$ and $T_{2}$ are related by $T_{1} = \sqrt{3} T_{2}$ . The angle $θ_{1}$ and $θ_{2}$ are [2025]

1 $θ_{1} = 30 °, θ_{2} = 60 ° with T_{2} = \frac{3 m g}{4}$

2 $θ_{1} = 60 °, θ_{2} = 30 ° with T_{2} = \frac{m g}{2}$

3 $θ_{1} = 45 °, θ_{2} = 45 ° with T_{2} = \frac{3 m g}{4}$

4 $θ_{1} = 30 °, θ_{2} = 60 ° with T_{2} = \frac{4 m g}{5}$