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A metallic block of mass $20 \mathrm{~kg}$ is dragged with a uniform velocity of $0.5 \mathrm{~ms}^{-1}$ on a horizontal table for $2.1 \mathrm{~s}$. The co-efficient of static friction between the block and the table is $0.10$. What will be the maximum possible rise in temperature of the metal block if the specific heat of the block is $0.1$ C.G.S unit ? Assume $g=10 \mathrm{~ms}^{-2}$ uniform rise in temperature throughout the whole block. [lgnore absorption of heat by the table]
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Verified Answer
The correct answer is:
$0.0025^{\circ} \mathrm{C}$
Hint:
friction $f=\mu \mathrm{mg}=0.1 \times 20 \times 10=20$
$\mathrm{~W}_{\mathrm{f}}=$ heat
$\Rightarrow(\mathrm{f.u}) \mathrm{t}=\mathrm{mc} \Delta \mathrm{T}$
$\Rightarrow 20 \times 0.5 \times 2.1=20 \times 0.1 \times 4.2 \times 10^{3} . \Delta \mathrm{T}$
$\Rightarrow \Delta \mathrm{T}=0.0025^{\circ} \mathrm{C}$
friction $f=\mu \mathrm{mg}=0.1 \times 20 \times 10=20$
$\mathrm{~W}_{\mathrm{f}}=$ heat
$\Rightarrow(\mathrm{f.u}) \mathrm{t}=\mathrm{mc} \Delta \mathrm{T}$
$\Rightarrow 20 \times 0.5 \times 2.1=20 \times 0.1 \times 4.2 \times 10^{3} . \Delta \mathrm{T}$
$\Rightarrow \Delta \mathrm{T}=0.0025^{\circ} \mathrm{C}$
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