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If the work done in blowing a soap bubble of radius $\mathrm{K}$ is W, then the work done in blowing the soap bubble of radius $2 R$ is
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Verified Answer
The correct answer is:
$4 \mathrm{~W}$
Work done is given by:
$$
\mathrm{W}=\mathrm{T} \cdot \mathrm{A}
$$
Area of spherical bubble is $4 \pi R^2$
$$
\text { i.e., } \mathrm{W}=\mathrm{T} \times 4 \pi \mathrm{R}^2 \text {. }
$$
$$
\mathrm{W} \propto \mathrm{R}^2
$$
For Radius R, Workdone $=\mathrm{W}$
For Radius $2 \mathrm{R}$, Workdone, $\mathrm{W}^{\prime}=(2 \mathrm{R})^2=4 \mathrm{R}^2$
$$
\mathrm{W}^{\prime}=4 \mathrm{~W}
$$
$$
\mathrm{W}=\mathrm{T} \cdot \mathrm{A}
$$
Area of spherical bubble is $4 \pi R^2$
$$
\text { i.e., } \mathrm{W}=\mathrm{T} \times 4 \pi \mathrm{R}^2 \text {. }
$$
$$
\mathrm{W} \propto \mathrm{R}^2
$$
For Radius R, Workdone $=\mathrm{W}$
For Radius $2 \mathrm{R}$, Workdone, $\mathrm{W}^{\prime}=(2 \mathrm{R})^2=4 \mathrm{R}^2$
$$
\mathrm{W}^{\prime}=4 \mathrm{~W}
$$
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