Question

Calculate the tension in the string BC as shown. ​

Answer 1

Answer:

2mgsintheta

this is the correct answer guyss!

Answer 2

Answer: Tension in the string is $\bold{2mg \ sin\theta}$.

Given: A block of mass m and a pully.

To Find: Tension in the string BC.

Step-by-step explanation:

Step 1: The concept of equilibrium or balance when dealing with forces is very fundamental. An object can generally be affected by multiple forces at once. Considering that a force is a vector quantity, it has both a magnitude (size) and a direction. There is no net force exerted on an object and it is considered to be in equilibrium if the amount and direction of the forces acting on it are precisely balanced. Newton's first law of motion states that an object at rest will remain at rest and an object in motion will remain in motion since there is no net force operating on an object in equilibrium.

Step 2: Using equilibrium of forces, we can get

$T=mg\ ...eq(1)\\\\T^{'}=2T=2mg\ ...eq(2)\\\\T_A\ sin\theta = T_C\ cos \theta\ ...eq(3)\\\\T_A=T_C\ cot \theta\ ...eq(4)$

Now at point B

$T_A\ cos \theta +T_C\ sin\theta = T^{'}$

From equation (2) and (4) we get,

$T_A\ cos\theta +T_C \ sin \theta = 2mg\\\\T_C\ cos \theta \ cot\theta +T_C \ sin \theta = 2mg\\\\T_C\ cos^2 +T_C \ sin^2 \theta = 2mg\ sin \theta\\\\T_C = 2mg\ sin \theta$

Hence, tension in the string is $\bold{2mg \ sin\theta}$.

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