JEE MAIN - Physics (2004 - No. 42)
A uniform chain of length $$2$$ $$m$$ is kept on a table such that a length of $$60$$ $$cm$$ hangs freely from the edge of the table. The total mass of the chain is $$4$$ $$kg.$$ What is the work done in pulling the entire chain on the table?
$$12$$ $$J$$
$$3.6$$ $$J$$
$$7.2$$ $$J$$
$$1200$$ $$J$$
Explanation
Mass of hanging part $$(m') = {4 \over 2} \times \left( {0.6} \right)kg$$ = 1.2 kg
Let at the surface $$PE=0$$
Center of mass of hanging part $$=0.3$$ $$m$$ below the surface of the table
$${U_i} = - m'gx = - 1.2 \times 10 \times 0.30$$ = - 3.6 J
$$\Delta U = m'gx = 3.6 J = $$ Work done in putting the entire chain on the table.
Let at the surface $$PE=0$$
Center of mass of hanging part $$=0.3$$ $$m$$ below the surface of the table
$${U_i} = - m'gx = - 1.2 \times 10 \times 0.30$$ = - 3.6 J
$$\Delta U = m'gx = 3.6 J = $$ Work done in putting the entire chain on the table.
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