Question

A uniform chainof length 2m is kept on a tabke such that a length of 60cm hangs freely from the edge of the table . the total mass of the chain is 4kg . what is the work done in pulling the entire chain on the table ? [AIEEE 2004] ​

Answer 1

Given:-

• Total Mass of Chain = 4kg.

• Length of chain kept on table = 2m.

• Length of chain hangs freely = 60cm→ 0.6m

To Find:-

• The work done in Pulling the entire Chain on the table.

Formulae used:-

• Potential energy ( Work done ) = mgh

Where,

• m = Mass
• g = Acceleration due to gravity.
• h = Height

Now,

→ Mass Per length = $\sf{\dfrac{m}{l}}$

→ Mass Per length = $\sf{\dfrac{4}{2}}$

→ Mass Per length = 2kg/m.

So,

→ Mass of chain lying freely = 0.6 × 2

→ Mass of chain lying freely = 1.2kg

Therefore,

→ The center of mass of Hanging Part = $\sf{\dfrac{0.6}{2}}$ → 0.3m.

Hence,

→ $\text{Work done on Pulling the Chain on the table = mgh}$

→ Work Done = 1.2 × 10 × 0.3 → 3.6J.

Hence, The Work done is 3.6J.

Answer 2

$\large\sf{\underline{\underline{\orange{Given}}}}$

↪ Total Mass of chain = 4kg

↪ Length of chain kept on table = 2m

↪ Length of chain hangs freely = 60cm → 0.6m

$\large\sf{\underline{\underline{\orange{Solution}}}}$

⟹ Mass per length = $\dfrac{m}{l} = \dfrac{4}{2}$

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀= 2kg/m

⟹ Mass of chain lying freely = 0.6 × 2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 1.2kg

⟹ The center of mass of hanging part

⟹ $\dfrac{0.6}{2}$

⟹ 0.3m

By using formulae

$\large{\boxed{\purple{Potential\: energy = mgh}}}$

⟹ Work done = 1.2 × 10 × 0.3

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3.6 J

★ Therefore the work done in pulling the entire chain on the table is 3.6J .