Question

Calculate the tension in the rope of mass M, length
L at the given point P as shown in the figure
​

Answer 1

To find:

Tension in the rope of mass M, length L at the given point P?

Calculation:

• Refer to Free Body diagram as attached.

Since point P is at equilibrium, we can say that:

$T_{P} = mg + M_{(shaded \: rod)}g$

$\implies \: T_{P} = mg + ( \lambda l)g$

$\implies \: T_{P} = mg + \bigg \{\lambda (L - x)\bigg \}g$

$\implies \: T_{P} = mg + \bigg \{ \dfrac{M}{L} (L - x)\bigg \}g$

$\implies \: T_{P} = mg + Mg - \dfrac{Mxg}{L}$

$\implies \: T_{P} = \bigg \{ m+ M - \dfrac{Mx}{L} \bigg \}g$

So, final answer is:

$\boxed{ \bold{\: T_{P} = \bigg \{ m+ M - \dfrac{Mx}{L} \bigg \}g}}$