Ice starts forming in lake with water at 0° C when the atmospheric temperature is -10° C. If the time taken for 1 cm of ice be 7 h, then the time taken (in hours) for the thickness of ice to change from 1 cm to 2 cm is

Question

Ice starts forming in lake with water at 0° C when the atmospheric temperature is -10° C. If the time taken for 1 cm of ice be 7 h, then the time taken (in hours) for the thickness of ice to change from 1 cm to 2 cm is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

∵ t propto(x22-x12) For x1=0, x2=1 cm , 7 propto(12-02) ...(i) For x1=1 cm , x2=2 cm , t propto(22-12) ...(ii) Solving (i) and (ii), we get ⇒ (7/t)=(1/3) t=21 h

Q. Ice starts forming in lake with water at $0^{\circ} C$ when the atmospheric temperature is $- 1 0^{\circ} C$ . If the time taken for $1 c m$ of ice be $7 h$ , then the time taken (in hours) for the thickness of ice to change from $1 c m$ to $2 c m$ is

$∵ t \propto (x_{2}^{2} - x_{1}^{2})$
For $x_{1} = 0, x_{2} = 1 c m$ ,
$7 \propto (1^{2} - 0^{2})$ ...(i)
For $x_{1} = 1 c m, x_{2} = 2 c m$ ,
$t \propto (2^{2} - 1^{2})$ ...(ii)
Solving (i) and (ii), we get
$\Rightarrow \frac{7}{t} = \frac{1}{3} t = 21 h$

Q. Ice starts forming in lake with water at 0∘C when the atmospheric temperature is −10∘C. If the time taken for 1cm of ice be 7h, then the time taken (in hours) for the thickness of ice to change from 1cm to 2cm is

∵t∝(x22​−x12​) For x1​=0,x2​=1cm , 7∝(12−02) ...(i) For x1​=1cm,x2​=2cm , t∝(22−12) ...(ii) Solving (i) and (ii), we get ⇒t7​=31​t=21h

Q. Ice starts forming in lake with water at $0^{\circ} C$ when the atmospheric temperature is $- 1 0^{\circ} C$ . If the time taken for $1 c m$ of ice be $7 h$ , then the time taken (in hours) for the thickness of ice to change from $1 c m$ to $2 c m$ is

$∵ t \propto (x_{2}^{2} - x_{1}^{2})$
For $x_{1} = 0, x_{2} = 1 c m$ ,
$7 \propto (1^{2} - 0^{2})$ ...(i)
For $x_{1} = 1 c m, x_{2} = 2 c m$ ,
$t \propto (2^{2} - 1^{2})$ ...(ii)
Solving (i) and (ii), we get
$\Rightarrow \frac{7}{t} = \frac{1}{3} t = 21 h$