Derive an expression for the radius of rope used in a crane to lift the mass M kg. The elastic limit of the material of rope is σ N/m², and safety factor of crane is K.

Solution

Given mass = M kg
Elastic limit of the material = σ N/m²

Safety factor for crane = K

The design of the rope is such that it should tolerate a load of KM kg.
Let r be the radius of rope required to be used in the crane.
So, using the formula,

Elastic limit = \frac{Maximum load}{Area of cross section} i . e . σ = \frac{KMg}{{πr}^{2}} ∴ r = \sqrt{\frac{KMg}{πσ}}

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Derive an expression for the radius of rope used in a crane to lift the mass M kg. The elastic limit of the material of rope is σ N/m², and safety factor of crane is K.

Some More Questions From Mechanical Properties of Fluids Chapter

What is the nature of inter-atomic or inter-molecular forces?

Which force is more stronger-interatomic or intermolecular force?

Define rigid body.

Which state of matter possesses rigidity?

What is elasticity?

Name the property of material that opposes the deformation in it.

Name the quantity which has neither unit nor dimensions.

Why strain is dimensionless?

What is stress?

Name the two types of stress.

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Mechanical Properties Of Fluids

Derive an expression for the radius of rope used in a crane to lift the mass M kg. The elastic limit of the material of rope is σ N/m2, and safety factor of crane is K.

Some More Questions From Mechanical Properties of Fluids Chapter

What is the nature of inter-atomic or inter-molecular forces?

Which force is more stronger-interatomic or intermolecular force?

Define rigid body.

Which state of matter possesses rigidity?

What is elasticity?

Name the property of material that opposes the deformation in it.

Name the quantity which has neither unit nor dimensions.

Why strain is dimensionless?

What is stress?

Name the two types of stress.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Derive an expression for the radius of rope used in a crane to lift the mass M kg. The elastic limit of the material of rope is σ N/m², and safety factor of crane is K.