31. Rate of heat flow through a cylindrical rod is $${H_1}.$$ Temperatures of ends of rod are $${T_1}$$ and $${T_2}.$$ If all the dimensions of rod become double and temperature difference remains same and rate of heat flow becomes $${H_2}.$$ Then,
A
$${H_2} = 2{H_1}$$
B
$${H_2} = \frac{{{H_1}}}{2}$$
C
$${H_2} = \frac{{{H_1}}}{4}$$
D
$${H_2} = 4{H_1}$$
Answer :
$${H_2} = 2{H_1}$$
32.
Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is $${100^ \circ }C,$$ then the temperature difference between the ends of other diagonal will be
(where $$l$$ is the length of each rod)
A
$${0^ \circ }C$$
B
$${\frac{{100}}{l}^ \circ }C$$
C
$${\frac{{100}}{{2l}}^ \circ }C$$
D
$${100^ \circ }C$$
Answer :
$${0^ \circ }C$$
33. Three rods of identical cross - sectional area and made from the same metal from the sides of an isosceles triangle $$ABC,$$ right - angled at $$B.$$ The points $$A$$ and $$B$$ are maintained at temperatures $$T$$ and $$\left( {\sqrt 2 } \right)$$ $$T$$ respectively. In the steady state, the temperature of the point $$C$$ is $${T_c}.$$ Assuming that only heat conduction takes place, $$\frac{{{T_c}}}{T}$$ is
A
$$\frac{1}{{2\left( {\sqrt 2 - 1} \right)}}$$
B
$$\frac{3}{{\sqrt 2 + 1}}$$
C
$$\frac{1}{{\sqrt 3 \left( {\sqrt 2 - 1} \right)}}$$
D
$$\frac{1}{{\sqrt 2 + 1}}$$
Answer :
$$\frac{3}{{\sqrt 2 + 1}}$$
34. If two rods $$A$$ and $$B$$ of equal length $$L,$$ and different areas of cross-section $${A_1}$$ and $${A_2}$$ have one end each at temperature $${T_1}$$ and $${T_2},$$ have equal rates of flow of heat, then
A
$${A_1} = {A_2}$$
B
$$\frac{{{A_1}}}{{{A_2}}} = \frac{{{K_1}}}{{{K_2}}}$$
C
$$\frac{{{A_1}}}{{{A_2}}} = \frac{{{K_2}}}{{{K_1}}}$$
D
$${K_1} = {K_2}$$
Answer :
$$\frac{{{A_1}}}{{{A_2}}} = \frac{{{K_2}}}{{{K_1}}}$$