Physics-
General
Easy
Question
Six identical metallic rods are joined together in a pattern as shown in the figure. Points A and D are maintained at temperature
and
. The temperature of the junction
will be
![](data:image/png;base64,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)
The correct answer is: ![120 ℃](data:image/png;base64,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)
![R equals fraction numerator l over denominator K A end fraction](data:image/png;base64,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)
![fraction numerator T subscript A end subscript minus T subscript B end subscript over denominator R end fraction equals fraction numerator T subscript B end subscript minus T subscript C end subscript over denominator R end fraction equals fraction numerator T subscript C end subscript minus T subscript D end subscript over denominator R end fraction](data:image/png;base64,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)
(i)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/902115/1/936379/Picture911.png)
(ii)
Solving (i) and (ii)
![T subscript B end subscript equals 120 ℃](data:image/png;base64,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)
Related Questions to study
physics-
Which curve shows the rise of temperature with the amount of heat supplied, for a piece of ice?
![](data:image/png;base64,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)
Which curve shows the rise of temperature with the amount of heat supplied, for a piece of ice?
![](data:image/png;base64,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)
physics-General
physics-
The graph signifies
![](data:image/png;base64,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)
The graph signifies
![](data:image/png;base64,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)
physics-General
physics-
The figure given below shows the cooling curve of pure wax material after heating. It cools from
to
and solidifies along
If
and
are respective values of latent heat and the specific heat of the liquid wax, the ratio
is
![](data:image/png;base64,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)
The figure given below shows the cooling curve of pure wax material after heating. It cools from
to
and solidifies along
If
and
are respective values of latent heat and the specific heat of the liquid wax, the ratio
is
![](data:image/png;base64,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)
physics-General
physics-
One end of a thermally insulated rod is kept at a temperature
and other at
. The rod is composed of two sections of lengths
and
and thermal conductivities
and
respectively. The temperature at the interface of the two sections is
![](data:image/png;base64,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)
One end of a thermally insulated rod is kept at a temperature
and other at
. The rod is composed of two sections of lengths
and
and thermal conductivities
and
respectively. The temperature at the interface of the two sections is
![](data:image/png;base64,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)
physics-General
maths-
If
and theperiod of
is
, then ![n equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAKCAYAAACngj4SAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHdJREFUeNpjYECAeiAuAWJxIJ4PxN+A+B0Q5zHQCKyCGg6yzB6ImYBYGoh/ADEXDj3/icA4wS0gTsMiDvKlMLV9B/LNFyziLNCgpTowB+L9WMQtcYhTHKSR0LgjVpxiMAmIk0kQpxisA2IvEsQpBqCUyEGC+NABALFuJtRrdbDQAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5uPC9taT48bW8+PTwvbW8+PC9tYXRoPteeGUsAAAAASUVORK5CYII=)
If
and theperiod of
is
, then ![n equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAKCAYAAACngj4SAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHdJREFUeNpjYECAeiAuAWJxIJ4PxN+A+B0Q5zHQCKyCGg6yzB6ImYBYGoh/ADEXDj3/icA4wS0gTsMiDvKlMLV9B/LNFyziLNCgpTowB+L9WMQtcYhTHKSR0LgjVpxiMAmIk0kQpxisA2IvEsQpBqCUyEGC+NABALFuJtRrdbDQAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5uPC9taT48bW8+PTwvbW8+PC9tYXRoPteeGUsAAAAASUVORK5CYII=)
maths-General
physics-
The adjoining diagram shows the spectral energy density distribution
of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature
is
![](data:image/png;base64,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)
The adjoining diagram shows the spectral energy density distribution
of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature
is
![](data:image/png;base64,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)
physics-General
physics-
Five identical rods are joined as shown in figure. Point
and
are maintained at temperature
and
respectively. The temperature of junction
will be
![](data:image/png;base64,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)
Five identical rods are joined as shown in figure. Point
and
are maintained at temperature
and
respectively. The temperature of junction
will be
![](data:image/png;base64,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)
physics-General
Maths-
If
, then
_______________
If
, then
_______________
Maths-General
physics-
Which one of the following is
graph for perfectly black body?
is the frequency of radiation with maximum intensity,
is the absolute temperature.
![](data:image/png;base64,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)
Which one of the following is
graph for perfectly black body?
is the frequency of radiation with maximum intensity,
is the absolute temperature.
![](data:image/png;base64,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)
physics-General
physics-
Three rods made of same material and having same cross-section are joined as shown in the figure. Each rod is of same length. The temperature at the junction of the three rods is
![](data:image/png;base64,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)
Three rods made of same material and having same cross-section are joined as shown in the figure. Each rod is of same length. The temperature at the junction of the three rods is
![](data:image/png;base64,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)
physics-General
physics-
The figure shows a glass tube (linear co-efficient of expansion is
) completely filled with a liquid of volume expansion co-efficient
On heating length of the liquid column does not change. Choose the correct relation between
and ![alpha](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAJVJREFUeNpjYEAFwkC8EIh/QGkeJDkQPxRZMRsQHwViLyh7PxBPgcrJA/E5NMMZaoG4EolvAMR3oeylQGyLruExmhNA4CAQuwHxNHTFxkB8mAETJAPxcSwGgT2zHIuGhVB/YYAgIF6HJjYbiBOhNquga+AD4vtArAbEgkA8H4hnQuW2QQMEA8hDg/IcWnjHA/ElBnIBAHRLGk6b6b/RAAAAT3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT4mI3gzQjE7PC9taT48L21hdGg+O57raQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
The figure shows a glass tube (linear co-efficient of expansion is
) completely filled with a liquid of volume expansion co-efficient
On heating length of the liquid column does not change. Choose the correct relation between
and ![alpha](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAJVJREFUeNpjYEAFwkC8EIh/QGkeJDkQPxRZMRsQHwViLyh7PxBPgcrJA/E5NMMZaoG4EolvAMR3oeylQGyLruExmhNA4CAQuwHxNHTFxkB8mAETJAPxcSwGgT2zHIuGhVB/YYAgIF6HJjYbiBOhNquga+AD4vtArAbEgkA8H4hnQuW2QQMEA8hDg/IcWnjHA/ElBnIBAHRLGk6b6b/RAAAAT3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT4mI3gzQjE7PC9taT48L21hdGg+O57raQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
physics-General
physics-
The spectrum of a black body at two temperatures
and
is shown in the figure. Let
and
be the areas under the two curves respectively. The value of
is
![](data:image/png;base64,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)
The spectrum of a black body at two temperatures
and
is shown in the figure. Let
and
be the areas under the two curves respectively. The value of
is
![](data:image/png;base64,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)
physics-General
physics-
In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures
and
The liquid columns in the two arms have heights
and
respectively. The coefficient of volume expansion of the liquid is equal to
![](data:image/png;base64,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)
In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures
and
The liquid columns in the two arms have heights
and
respectively. The coefficient of volume expansion of the liquid is equal to
![](data:image/png;base64,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)
physics-General
physics-
A bimetallic strip consists of metals
and
. It is mounted rigidly at the base as shown. The metal
has a higher coefficient of expansion compared to that for metal
. when bimetallic strip is placed in a cold bath
![](data:image/png;base64,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)
A bimetallic strip consists of metals
and
. It is mounted rigidly at the base as shown. The metal
has a higher coefficient of expansion compared to that for metal
. when bimetallic strip is placed in a cold bath
![](data:image/png;base64,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)
physics-General
physics-
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity
and 2
and thickness
and 4
, respectively are
and
. The rate of heat transfer through the slab, in a steady state is
, with
equals to
![](data:image/png;base64,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)
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity
and 2
and thickness
and 4
, respectively are
and
. The rate of heat transfer through the slab, in a steady state is
, with
equals to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAACzCAYAAADPCl20AAANoElEQVR4nO3d208Ud+PH8c/s7BFkF3BBoJZ1XU5G0UhBIoTiIVhTjbQXTaSpaZrYmPS2l/0HvGrSm9552xprWqNVk2oFmgCpUhURkbIc3MoiIKc9Mwu7z0UDvxLt85tld13m+3xeVyo73/kOvHd2ZmcWpXg8HgeRQHSZngBRqjFqEg6jJuEwahIOoybhMGoSTlJR+/1+TExMwO/3p2o+RElLKurZ2VncuXMH8/Pza/8Wi8UQCoWwsLCQ9OSINkKfzMLhcBhzc3OIRCKIxWLw+XwYHR3F6Ogo8vPzceTIkbXH9vX1IRwOo7i4GHNzc/D7/Xj33XdfGTMSiSAajcJoNMJkMv3rupeXlxEMBmE0GmGxWJLZjIzq7OzEnj17sHXr1kxPZUNisRhmZ2dhs9lgMBggSRIA4M8//0QwGMT+/fvf+JySihoA4vE4FhYW8PTpUzx+/Bj379/H9PQ0ampqsH//fsiyjOzsbCiKguvXr6OwsBBzc3M4cODAa8ebnp7Gw4cPkZubC4fDAavVCr/fj/n5eezbtw+KouDly5d4/vw5xsbGsHfvXuzatSvZzUi7aDSKQCAARVFgt9sxOzsLvV6Pq1evoqCgQLNRK4qCGzduYPv27XA4HNi2bRuys7Px+PFjTE5OajPqcDiMe/fuwev14vnz538PqtfD6/Xi119/hcViQXNzM+rq6tDf348LFy7g1KlTOHTo0LpxZmdnEY/HMTIygtu3byMUCsHlcqGyshITExMYHx/Hl19+iYmJCXR1dWFwcBCRSAQGgwEFBQXJbkbamEwmWCwWRKNR9Pb2wuPx4Pjx4/jhhx9QW1uLlZWVV5ZZWlrSzHlKMBhEZ2cnotEoXC4X6urqUFlZCZ/Ph1gslpE5JR316t4nEAjAaDTCbDZDlmUEAgGMjIxAkiTU19fDYDDAaDQiPz8fOp1u3QbH43HcunULkUgEk5OTCIVC8Pv9ePToEfr6+hAMBmEymfDdd9+hr68PKysriMVi0Ol06O/vh8/nS3Yz0sbhcKCmpgY2mw07duzAlStXMDs7i97eXpw9exZXr159ZZmXL1/i9u3b0MJtOYqiQFEULC8vY2hoCENDQ3A4HAgEAti5c2dG5pR01IWFhWhpaYHBYEB7ezt6e3uxsrKCgwcP4uzZs2uPWz08aWlpQSwWQ3d3N1paWta+XlRUBJ/Ph1AoBEmSIEkSDAYDZFlGPB6H0WiE3W5HVlYWIpEIFEWBJEnIyspCbm5uspuRNkajce0J7HA4cPr0aZw5cwbff/89zGbzvy6zbds2RCKRNznVDVlaWoJO9/f7DbIsw2QywWazQafTrR1fv2lJRw38vTFlZWVwOBw4fPgwurq6sGXLlnWPGRoawgcffIB9+/ZhaGgIT58+XfuaJElobm5GPB7HH3/8AbfbDaPRiLq6OlRXV2N4eBj9/f04c+YMTp06hY6ODvz2229YWFhAdXU1jh07lorNSIvVJygAzMzMoLOzE7W1tbh06RL27dv32mXsdvum3qZ/8vv9+OWXX6DT6VBXV4dDhw7B5XLh+vXrePHiRUbmlJKoV39wRqMRTqcT27dvf+Ux7733HmRZhl6vx+7du1FVVfXaMZxOJz755BPY7XbY7XaEQiG43W5IkgRZlpGbm4v3338fTU1NGB4exltvvbW2p9jMfD4fenp6MDIygq+//hrnz59He3s7QqHQK4/95xNhs7NYLGhra0N5eTm2bt26dviZyfknFbXNZoPT6YTNZvu/AfV66PWvDvvPl1qDwQCDwfDaMXNzc2G1WiHLMmRZhqIo676u0+lgNpthNBphtVo1ETQAZGVl4ejRo6ivr0dJSQm++uorZGdno729PdNTS4rBYEBDQwNMJhNkWc70dAAkGfWzZ8+gKAp6enpgNBoTWlbtMzkajSIUCsFut+PmzZspG3cjEh373x4/ODi49mePx4Oenp61d45SPYdEpHLsJ0+e/NfrDOmUVNT37t2Dy+VCfn4+AKTtbN1oNGJkZORf39tORqbfYfjoo4+Ql5eX8AUkNfOWJClj22cymeBwODKy7qSiVhQFu3btSvitm0S/0ZOTk+jt7cXBgwfTMr5amX4CrNLC9s3PzyMnJydl4yUiJSeKidrIy3giJ09aOckSWSaPr7VxlkWUAE1FvVle/mlz01TURGowahIOoybhMGoSDqMm4TBqEg6jJuEwahKOZqLmpW9SSzNRE6mlqah5mZzU0FTURGowahIOoybhMGoSDqMm4TBqEg6jJuEwahIOoybhMGoSjmaizuRvGyJt0UzURGoxahIOoybhMGoSDqMm4TBqEg6jJuEwahIOoybhMGoSjiaiXv2vMXiZnNTQRNREiWDUJBxGTcJh1CQcRk1pk6kTe0ZNwmHUJJykoo7FYqmaB1HKcE9NwmHUJBzNRM3L5KSWZqImUotRk3AYNQmHUZNwGDUJh1GTcBg1CYdRk3AYNQmHUZNwNBO1JEmZngJphGaiJlJLv/qHeDyOxcVFXLlyBV6vFydPnkRlZSVMJlMm57cOb2giNdbtqXU6HSoqKmC32+HxeBCNRjM1L6INW9tTS5IEq9WK8vJyTE5OorS0FHq9/r8tS6RaNBrF8PAwAGDnzp0wm81pW9fanjoejyMYDOLGjRvw+XzIzs5m1JQSsVgMPp8P3d3duHbtGrxeb1qPAtZFPT09jfv378Pj8WBychLLy8spXVkgEMDExATcbjc8Hg+CwWBKx99swuEwvF4vFhYWEA6H8fz5c4yPjyMej8Pv92Nqairl3+PNKBaLIR6P48SJEygsLITH44GiKGlb39quWKfTwel04ptvvnntpJaWlhCJRNb+zWQyJfzB24GBAdy6dQuSJCESiaC1tRW1tbVJTH9zGxsbw6VLl9DY2Ii8vDxcvnwZRUVF+OKLL9DX14fe3l58+umnyMvLy/RU00qv1yM/Px/z8/OYnp7G8ePHYbFY0rc+NQ8KBALo7u7G3bt3oSgKZFnGgQMHEA6HE1rZxMQE6uvr0dTUhIcPH2JkZEToqIeGhpCbmwu3243h4WE0NzejtbU1rXupzSoQCODbb7/FZ599BrvdDp0ufe8mqxo5JycHx44dw7lz5yDLMmpqanDkyBFkZ2cntLLW1lYcPXoUHo8HXV1dwu+h+vv78fPPP+Py5ct45513cPLkyUxPKSOWlpYwMjKCaDSKCxcuYGBgAEtLS2lbn6o99ervh47FYhgfH8fHH38Mg8GQ8MpkWcaDBw9w8+ZNvP3222hqakp4DK2IRqPo7++H0+lEYWEh3G43AoEAbDZbpqf2xhmNRuzZswculwsAYLFY0vomREKvAdFoFFNTUygtLYUsywmv7M6dO/jxxx9RU1ODEydOpPW4KtP++usvFBUVoa2tDW1tbTCZTOjo6Mj0tDJCkiQYDAZYrVZYrVYYDIa12x5mZmZw6dIlXLt2DYuLi/jpp59w7ty5dedviVIddTQaxcLCAvLy8mAymRK+F2NwcBAXL15EJBLB/Pw83G43QqGQ6uW1du/H4OAgnE4nnE4nysrKUF1djY6ODrjd7kxP7Y1Q+/Pyer0YHx+Hoii4fPkynjx5gs8//3xDRwKrVL8GRCIReDwelJWVbWhFNpsNH374IQDAarXCbDYntLePx+OaukzucrngcrlQWFgIs9mMmpoabNmyBTk5OZme2qby7NkzDAwMYHx8HPn5+Whra8Pu3buTGlN11MvLy/D5fKivr9/QXrOkpAQlJSUJL6dVVVVV6/5eXFyM4uJiAPiffPfjdWKxGMbGxuDxeFBRUYFwOIwdO3YkPa7qww+z2YzGxkY0NDRo7lBgs9HpdCgoKEBVVdWmumHsTfP7/VhcXERjYyNOnz4NSZJw9+7dpMdVvae2WCxwOBxJr5D+vhhRWVmJysrKTE8loyYmJmA2m3H48GHU1NRAp9Ph4sWL2Lt3L/Lz8ze889TM/dR8dRDPwsICCgoK4HA4kJ2djfLycthsNjx48AArKysbHpd3LFHGNDQ0oKGhYe3vJSUlOH/+fNLjamZPTaQWoybhMGoSDqMm4TBqEo6motbSZXLKHE1FTaQGoybhMGoSDqMm4TBqEg6jJuEwahIOoybhMGoSjiaiXv29I0RqaCLqVVr7RPn/ukz9rDQVNZEajJqEw6hJOIyahMOoSTiMmoTDqEk4jJqEw6hJOJqJmpfJSS3NRE2kFqMm4TBqEg6jJuEwahKOpqLmvdSkhqaiJlKDUZNwGDUJh1GTcBg1CUczUfPeD1JLM1ETqcWoSTiMmoTDqEk4jJqEw6hJOIyahMOoSTiMmoTDqEk4molakiR+SIBU0UzURGoxahIOoybhMGoSDqMm4TBqEo4+mYUXFxfx6NEjvHjxIuFlE/kky/z8PEZHR/H777/DYrEkvK5UzGGzjJ3uTwClavypqSk4nc6UjJWopKKuq6tDMBiE1+tN23vIkiRhaWkJFRUVmJmZgU6nE+6jXavbo+Z7qJVtz8vLQ2lpaUbWLcVTWGM6L46ka2ytjbuRsTOxjXq9HrIsp2W9/5+URk20GfBEkYTDqEk4jJqEw6hJOIyahMOoSTiMmoTDqEk4jJqEw6hJOIyahMOoSTiMmoTDqEk4jJqEw6hJOIyahMOoSTiMmoTDqEk4jJqEw6hJOIyahPMfklVon4/wWmQAAAAASUVORK5CYII=)
physics-General