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Question

A uniform rope of length L and mass M is hanging from a rigid support. The tension in the rope at a distance x from the rigid support is

A
Mg
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B
Mg(LxL)
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C
Mg(LLx)
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D
Mg(xL)
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Solution

The correct option is B Mg(LxL)

Since the rope is uniform, mass per unit length for the rope remain same at each section.
Therefore ML=mLx(Lx)
mLx=M(LxL)
From the FBD,

T=(mLx)g=M(LxL)g
Hence, tension in the rope at a distance x from the rigid support T=M(LxL)g

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