Question

Select the correct option given below:
Rays from the sun are focused by a lens of diameter $5cm$ on to a block of ice and $10g$ of ice is melted in $20$ min.Therefore the heat from the sun reaching the earth per min per square centimetre is (Latent heat of ice L$=80cal{g}^{-1}$)

• A. $2.04cal$
• B. $0.51cal$
• C. $4.08cal$
• D. $3.02cal$

Answer 1

The correct option is A $2.04cal$

If $s$ calorie of heat is received from the sun per $c{m}^2$ prr minute, the heat collected by the lens of radius$2.5cm$ in $20$minutes is
$Q_1=s\times A\times t$

$\Rightarrow s\times \pi \times (2.5{)}^2\times (20)$

$\Rightarrow \left(392.5\right)scal$

Heat required to melt $10g$ of ice is
$Q_2=mL$

$\Rightarrow 10\times 80=800cal$

According to given problem $Q_1=Q_2$

$\therefore 392.5s=800$

or $s=2.04calc{m}^{-2}mi{n}^{-1}$