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Solve the following :

Question:

A block of mass $100 \mathrm{~g}$ is moved with a speed of $5.0 \mathrm{~m} / \mathrm{s}$ at the highest point in a closed circular tube of radius $10 \mathrm{~cm}$ kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

Solution:

Work done by block

$=$ T.E at $A-$ T.E. at $B$

$=\frac{1}{2} \mathrm{mv}^{2}+\mathrm{mgh}-0$

$=\frac{1}{2} \times 0.1 \times 5^{2}+0.1 \times 10 \times 0.2$

$W=1.45 \mathrm{~J}$

Work done by tube $=$ - Work done by block

$W^{\prime}=-1.45 \mathrm{~J}$

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