Question
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then
![](data:image/png;base64,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)
The correct answer is: ![u subscript 1 end subscript less than u subscript 2 end subscript](data:image/png;base64,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)
Maximum height and time of flight depend on the vertical component of initial velocity
![H subscript 1 end subscript equals H subscript 2 end subscript rightwards double arrow u subscript y end subscript subscript 1 end subscript equals u subscript y end subscript subscript 2 end subscript](data:image/png;base64,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)
Here ![T subscript 1 end subscript equals T subscript 2 end subscript](data:image/png;base64,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)
Range ![R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 blank theta over denominator g end fraction equals fraction numerator 2 left parenthesis u sin invisible function application theta right parenthesis left parenthesis u cos invisible function application theta right parenthesis over denominator g end fraction](data:image/png;base64,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)
![equals fraction numerator 2 u subscript x end subscript u subscript y end subscript over denominator g end fraction](data:image/png;base64,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)
![R subscript 2 end subscript greater than R subscript 1 end subscript therefore u subscript x subscript 2 end subscript end subscript greater than u subscript x subscript 1 end subscript end subscript blank o r blank u subscript 2 end subscript greater than u subscript 1 end subscript](data:image/png;base64,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)
Related Questions to study
A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and ![g equals 10 m s to the power of negative 2 end exponent](data:image/png;base64,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)
![](data:image/png;base64,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)
A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and ![g equals 10 m s to the power of negative 2 end exponent](data:image/png;base64,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)
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The equation of the circumcircle of the triangle formed by the lines
and y=0 is
The equation of the circumcircle of the triangle formed by the lines
and y=0 is
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown
![](data:image/png;base64,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)
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown
![](data:image/png;base64,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)
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
![](data:image/png;base64,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)
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
![](data:image/png;base64,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)
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
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)
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
![](data:image/png;base64,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)
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Pole and polar are one of the important parts of the circle, many questions can be based on these parts. It should be remembered that while writing the equation of polar for a pole, the coefficients of square terms in the equation of the circle is one. If the equation of the circle does not have coefficients as one, then make it one before solving the question.
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Pole and polar are one of the important parts of the circle, many questions can be based on these parts. It should be remembered that while writing the equation of polar for a pole, the coefficients of square terms in the equation of the circle is one. If the equation of the circle does not have coefficients as one, then make it one before solving the question.
Three rods of equal length
are joined to form an equilateral triangle
O is the mid point of
Distance
remains same for small change in temperature. Coefficient of linear expansion for
and
is same,
but that for
is
Then
![](data:image/png;base64,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)
Three rods of equal length
are joined to form an equilateral triangle
O is the mid point of
Distance
remains same for small change in temperature. Coefficient of linear expansion for
and
is same,
but that for
is
Then
![](data:image/png;base64,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)
A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458151/1/936836/Picture70.png)
A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458151/1/936836/Picture70.png)
One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
a) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487012/1/936835/Picture58.png)
b) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487012/1/936835/Picture61.png)
c) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487012/1/936835/Picture64.png)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458144/1/936835/Picture67.png)
One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
a) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487012/1/936835/Picture58.png)
b) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487012/1/936835/Picture61.png)
c) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487012/1/936835/Picture64.png)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458144/1/936835/Picture67.png)
Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?
![](data:image/png;base64,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)
Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?
![](data:image/png;base64,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)
Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures
![](data:image/png;base64,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)
Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures
![](data:image/png;base64,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)
The area of circle centred at (1, 2) and passing through (4, 6) is
The area of a circle is the space occupied by the circle in a two-dimensional plane. Area of circle = πr2 (π = 22/7).
The area of circle centred at (1, 2) and passing through (4, 6) is
The area of a circle is the space occupied by the circle in a two-dimensional plane. Area of circle = πr2 (π = 22/7).