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NEET NEET Questions — Free MCQ Practice

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Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B i.e. $r_{A} = 2 r_{B}$ . For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

A.

$K_{A} = 4 K_{B}$

B.

$K_{A} = 2 K_{B}$

C.

$K_{A} = K_{B} / 2$

D.

$K_{A} = K_{B} / 4$

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Explanation

(d) $\frac{Q}{t} = \frac{KA ∆ θ}{l} \Rightarrow \frac{K_{A}}{K_{B}} = \frac{A_{B}}{A_{A}} = {(\frac{r_{B}}{r_{A}})}^{2} = \frac{1}{4} \Rightarrow K_{A} = \frac{K_{B}}{4}$

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Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of composite plate will be

A.

5

B.

2.4

C.

1.5

D.

1.2

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Explanation

(b) Thermal conductivity of composite plate

$K_{eq} = \frac{2 K_{1} K_{2}}{K_{1} + K_{2}} = \frac{2 \times 2 \times 3}{2 + 3} = \frac{12}{5} = 2.4$

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The coefficients of thermal conductivity of copper, mercury and glass are respectively $K_{c}$ , $K_{m}$ and $K_{g}$ such that $K_{c} > K_{m} > K_{g}$ . If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $X_{c}$ , $X_{m}$ and $X_{g}$ , then

A.

$X_{c} = X_{m} = X_{g}$

B.

$X_{c} > X_{m} > X_{g}$

C.

$X_{c} < X_{m} < X_{g}$

D.

$X_{m} < X_{c} < X_{g}$

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Explanation

(c) $\frac{Q}{At} = K \frac{∆ θ}{l} \Rightarrow K \frac{∆ θ}{l} = constant \Rightarrow \frac{∆ θ}{l} \propto \frac{1}{K}$

Hence If $K_{c} > K_{m} > K_{g}$ , then

${(\frac{∆ θ}{l})}_{c} < {(\frac{∆ θ}{l})}_{m} < {(\frac{∆ θ}{l})}_{g} \Rightarrow X_{c} < X_{m} < X_{g}$

because higher K implies lower value of the temperature gradient.

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The quantity of heat which crosses unit area of a metal plate during conduction depends upon

A.

The density of the metal

B.

The temperature gradient perpendicular to the area

C.

The temperature to which the metal is heated

D.

The area of the metal plate

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Explanation

(b) $\frac{dQ}{dt} = KA \frac{dθ}{dl} \Rightarrow \frac{dQ}{dt} \propto \frac{dθ}{dl}$ (Temperature gradient)

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Two spheres of different materials one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting ice in the large radius one is 25 minutes and that for smaller one is 16 minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is

A.

4 : 5

B.

5 : 4

C.

25 : 1

D.

8 : 25

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Explanation

(d)

$For small sphere : radius = r and thickness = t Q_{s} = \frac{K_{s} 4 {πr}^{2} (∆ θ) t_{s}}{l} = m_{s} L = \frac{4}{3} {πr}^{3} \times ρ \times L For large sphere : radius = r and thickness = t Q_{L} = \frac{K_{L} 4 π {(2 r)}^{2} (∆ θ) t_{L}}{\frac{l}{4}} = m_{L} L = \frac{4}{3} π {(2 r)}^{3} \times ρ \times L \frac{Q_{S}}{Q_{L}} = \frac{K_{s} t_{s}}{16 K_{L} t_{L}} = \frac{1}{8} \Rightarrow \frac{K_{s}}{K_{L}} = \frac{1}{8} \times 16 \times \frac{25}{16} = \frac{25}{8} \Rightarrow \frac{K_{L}}{K_{S}} = \frac{8}{25}$

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Mud houses are cooler in summer and warmer in winter because

A.

Mud is superconductor of heat

B.

Mud is good conductor of heat

C.

Mud is bad conductor of heat

D.

None of these

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Explanation

(c) Mud is bad conductor of heat. So it prevents the flow of heat between surroundings and inside.

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The temperature of hot and cold end of a 20 cm long rod in thermal steady state are at 100 $° C$ and 20 $° C$ respectively. Temperature at the centre of the rod is

A.

50 $° C$

B.

60 $° C$

C.

40 $° C$

D.

30 $° C$

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Explanation

(b) Temperature gradient = $\frac{100 - 20}{20} = 4 ° C / cm$
temperature at centre = 100-4 $\times$ 10 = 60°C

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A heat flux of 4000 J/s is to be passed through a copper rod of length 10 cm and area of cross-section 100 ${cm}^{2}$ . The thermal conductivity of copper is 400 W/m $° C$ . The two ends of this rod must be kept at a temperature difference of

A.

1 $° C$

B.

10 $° C$

C.

100 $° C$

D.

1000 $° C$

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Explanation

(c) $∆ θ = \frac{Q \times l}{KAt} = \frac{4000 \times 0.1}{400 \times 10^{- 2}} = 100 ° C$

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At a common temperature, a block of wood and a block of metal feel equally cold or hot. The temperatures of block of wood and block of metal are

A.

Equal to temperature of the body

B.

Less than the temperature of the body

C.

Greater than temperature of the body

D.

Either (b) or (c)

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Explanation

(a) When the temperature of an object is equal to that of human body, no heat is transferred from the object to body and vice versa, Therefore block of wood and block of metal feel equally cold and hot if they have same temperature as human body.

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A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_{1}$ and $K_{2}$ . The equivalent conductivity of the combination is

A.

$K_{1} + K_{2}$

B.

$\frac{K_{1} + K_{2}}{2}$

C.

$\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}$

D.

$\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}$

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Explanation

(b) In parallel combination equivalent conductivity

$K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2} (As A_{1} = A_{2})$

NEET Practice Questions (MCQs) with Answers & Solutions

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