MCQ
Three containers $\mathrm{C}_{1}, \mathrm{C}_{2}$ and $\mathrm{C}_{3}$ have water at different temperatures. The table below shows the final temperature $T$ when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process)

$\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}$

The value of $\theta$ (in $^{\circ} \mathrm{C}$ to the nearest integer) is

  • A
    $45$
  • B
    $48$
  • C
    $55$
  • $50$

Answer

Correct option: D.
$50$
d
According to table and applying law of calorimetry

$1 \mathrm{T}_{1}+2 \mathrm{T}_{2}=(1+2) 60^{\circ}$

$=180$

$1 \mathrm{T}_{2}+2 \mathrm{T}_{3}=(1+2) 30^{\circ}$

$=90$

$2 \mathrm{T}_{1}+1 \mathrm{T}_{3}=(1+2) 60$

$=180$

$3\left(\mathrm{T}_{1}+\mathrm{T}_{2}+\mathrm{T}_{3}\right)=450$

$\mathrm{T}_{1}+\mathrm{T}_{2}+\mathrm{T}_{3}=150^{\circ}$

Hence,

$\mathrm{T}_{1}+\mathrm{T}_{2}+\mathrm{T}_{3}=(1+1+1) \theta$

$150=3 \theta$

$\theta=50^{\circ} \mathrm{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A liquid of mass $1$ $kg$ is filled in a flask as shown in figure. The force exerted by the flask on the liquid is $(g = 10\  m/s^2)$[Neglect atmospheric pressure]:
Vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other when $3 a+2 b=7$, the ratio of a to $b$ is $\frac{x}{2}$. The value of $x$ is $..............$
A particle experiences a variable force $\overrightarrow{ F }=\left(4 x \hat{ i }+3 y ^{2} \hat{ j }\right)$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $x-y$ plane, the Kinetic Energy changes by............$j$
A hemisspherical shell of mass $2M$ and radius $6R$ and a point mass $M$ are performing circular motion due to their mutual gravitational interaetion Their positions are shown in figure at any moment of time during motion. If $r_1$ and $r_2$ are the radii of circular path of hemispherical shell and point mass respectively and ${\omega _1}$ and  ${\omega _2}$ are the angular speeds of hemi-spherical shell and point mass respectively, then choose the correct option
You lift a heavy book from the floor of the room and keep it in the book-shelf having a height $2 \,m$. In this process you take $5\, seconds$. The work done by you will depend upon
A particle moving in a straight line covers half the distance with speed of $3 \,m/s$. The other half of the distance is covered in two equal time intervals with speed of $4.5 \,m/s$ and $7.5 \,m/s$ respectively. The average speed of the particle during this motion is...... $\,m/s$
If pressure at half the depth of a lake is equal to $2/3$ pressure at the bottom of the lake then what is the depth of the lake...... $m$
The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed  ......... $\%$
When a bicycle is in motion, the force of friction exerted by the ground on the two wheels is such that it acts
A planet revolving in elliptical orbit has

$(A)$ a constant velocity of revolution.

$(B)$ has the least velocity when it is nearest to the sun.

$(C)$ its areal velocity is directly proportional to its velocity.

$(D)$ areal velocity is inversely proportional to its velocity.

$(E)$ to follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below