First slide

Conduction

Question

A steam chamber is connected to an ice block at $0^{0} C$ , by means of two two identical rod in series . It is observed that 100 gm of ice is melted in 10 minutes. If they are connected in parallel amount ice melt in 5 minutes in gm is_

Moderate

A

200
B

400
C

100
D

50

Solution

$h e a t f l o w i s i n v e r s e l y p r o p o r t i o n a l t o r e s i s \tan c e a n d d i r e c t l y p r o p o r t i o n a l t o t i m e i n t h e f i r s t c a s e r e s i s \tan c e i s 2 R a n d t i m e i s 10 m i n i n t h e s e c o n d c a s e r e s i s \tan c e i s \frac{R}{2} a n d t i m e i s 5 m i n m \infty Q \infty \frac{t}{R} \frac{m_{1}}{m_{2}} = \frac{t_{1}}{t_{2}} \frac{R_{2}}{R_{1}} \frac{100}{m_{2}} = \frac{10}{5} \frac{\frac{R}{2}}{2 R} = \frac{1}{2} m_{2} = 200$

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