Question

In the figure show, if the system is in equilibrium then the value of M is ​

Answer 1

Given:

System is in equilibrium.

To find:

Value of mass M in terms of m ?

Calculation:

• Let the tension in the string be T .

• So, the tension from the two wires is holding up and keeping the weight of mass M balanced.

$\therefore \: T \cos( {60}^{ \circ} ) + T \cos( {60}^{ \circ} ) = Mg$

$\implies \: 2T \cos( {60}^{ \circ} ) = Mg$

• Now, the value of T will be equal to mg.

$\implies \: 2mg \cos( {60}^{ \circ} ) = Mg$

$\implies \: 2m\cos( {60}^{ \circ} ) = M$

$\implies \: 2m \times \dfrac{1}{2} = M$

$\implies \: M = m$

So, value of M is equal to m .

Answer 2

Tcosθ + Tcosθ = Mg

and, T = mg

⇒ T cos(60) + T cos(60) = Mg

⇒ 2T cos(60) = Mg

⇒ 2mg cos(60) = Mg

⇒ 2m x ½ = M

⇒ M = m

value of M is equal to m .