1

### JEE Main 2019 (Online) 11th January Evening Slot

Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
A
200oC
B
270oC
C
230oC
D
250oC

## Explanation

$\Delta {\ell _1} = \Delta {\ell _2}$

$\ell {\alpha _1}\Delta {T_1} = \ell {\alpha _2}\Delta {T_2}$

${{{\alpha _1}} \over {{\alpha _2}}} = {{\Delta {T_1}} \over {\Delta {T_2}}}$

${4 \over 3} = {{T - 30} \over {180 - 30}}$

$T = {230^o}C$
2

### JEE Main 2019 (Online) 11th January Evening Slot

When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be :
A
60oC
B
70oC
C
85oC
D
80oC

## Explanation

100 $\times$ SA $\times$ [100 $-$ 90] = 50 $\times$ SB $\times$ (90 $-$ 75)

2SA = 1.5 SB

SA = ${3 \over 4}$SB

Now, 100 $\times$ SA $\times$ [100 $-$ T] = 50 $\times$ SB (T $-$ 50)

2 $\times$ $\left( {{3 \over 4}} \right)$ (100 $-$ T) = (T $-$ 50)

300 $-$ 3T = 2T $-$ 100

400 = 5T

T = 80
3

### JEE Main 2019 (Online) 11th January Evening Slot

A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg–1 and 400 Jkg–1 K–1
A
20%
B
25%
C
15%
D
30%

## Explanation

0.1 $\times$ 400 $\times$ (500 $-$ T) = 0.5 $\times$ 4200 $\times$ (T $-$ 30) + 800 (T $-$ 30)

$\Rightarrow$  40(500 $-$ T) = (T $-$ 30) (2100 + 800)

$\Rightarrow$  20000 $-$ 40T = 2900 T $-$ 30 $\times$ 2900

$\Rightarrow$  20000 + 30 $\times$ 2900 = T(2940)

T = 30.4oC

${{\Delta T} \over T} \times 100$ = ${{6.4} \over {30}} \times 100$

$\simeq$ 20%
4

### JEE Main 2019 (Online) 11th January Evening Slot

A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in oC, if this thermometer in the contact with the object reads x0/2 ?
A
60
B
35
C
25
D
40

## Explanation $\Rightarrow$   ToC = ${{{x_0}} \over 6}$ & $\left( {{x_0} - {{{x_0}} \over 3}} \right)$ = (100 $-$ 0oC)

x0 = ${{300} \over 2}$

$\Rightarrow$  ToC = ${{150} \over 6}$ = 25oC