Physics-
General
Easy
Question
A small particle of mass
is projected at an angle
with the
-axis with an initial velocity
in the
-
plane as shown in the figure.
the angular momentum of the particle is
![](data:image/png;base64,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)
The correct answer is: ![negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack k with hat on top](data:image/png;base64,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)
Related Questions to study
physics-
The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is
![](data:image/png;base64,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)
The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is
![](data:image/png;base64,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)
physics-General
Maths-
If the normal at the point
to the ellipse
intersects it again at the point
, then
is
If the normal at the point
to the ellipse
intersects it again at the point
, then
is
Maths-General
physics-
A fighter plane enters inside the enemy territory, at time
with velocity
and moves horizontally with constant acceleration
(see figure). An enemy tank at the border, spot the plane and fire shots at an angle
with the horizontal and with velocity
. At what altitude
of the plane it can be hit by the shot?
![](data:image/png;base64,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)
A fighter plane enters inside the enemy territory, at time
with velocity
and moves horizontally with constant acceleration
(see figure). An enemy tank at the border, spot the plane and fire shots at an angle
with the horizontal and with velocity
. At what altitude
of the plane it can be hit by the shot?
![](data:image/png;base64,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)
physics-General
physics-
A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C</em
A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C</em
physics-General
physics-
A particle of mass
is rotating in a horizontal circle of radius
and is attached to a hanging mass
as shown in the figure. The speed of rotation required by the mass
keep
steady is
![](data:image/png;base64,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)
A particle of mass
is rotating in a horizontal circle of radius
and is attached to a hanging mass
as shown in the figure. The speed of rotation required by the mass
keep
steady is
![](data:image/png;base64,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)
physics-General
physics-
Figure shows the variation of the stopping potential (V0) with the frequency (v) of theincident radiations for two different photosensitive material M1 and M2 .What are the values of work functions for M1 and M2 respectively
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458522/1/937235/Picture73.png)
Figure shows the variation of the stopping potential (V0) with the frequency (v) of theincident radiations for two different photosensitive material M1 and M2 .What are the values of work functions for M1 and M2 respectively
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458522/1/937235/Picture73.png)
physics-General
physics-
The respective angles of the flint and crown glass prisms are
and A. They are to be used for dispersion without deviation, then the ratio of their angles
will be
The respective angles of the flint and crown glass prisms are
and A. They are to be used for dispersion without deviation, then the ratio of their angles
will be
physics-General
physics-
The two lines A and B shown in figure are the agraphs of the de Broglie wavelength l as function of
(V is the accelerating potential) for two particles having the same charge ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487038/1/937203/Picture70.png)
Which of the two represents the particle of heavier mass ?
The two lines A and B shown in figure are the agraphs of the de Broglie wavelength l as function of
(V is the accelerating potential) for two particles having the same charge ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487038/1/937203/Picture70.png)
Which of the two represents the particle of heavier mass ?
physics-General
physics-
In a photoelectric experiment anode potential is plotted against plate current
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458444/1/937196/Picture67.png)
In a photoelectric experiment anode potential is plotted against plate current
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458444/1/937196/Picture67.png)
physics-General
physics-
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure. Which of the following statements
is/are correct?
![](data:image/png;base64,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)
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure. Which of the following statements
is/are correct?
![](data:image/png;base64,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)
physics-General
Physics-
Two particles 1 and 2 are projected with same speed
as shown in figure. Particle 2 is on the ground and particle 1 is at a height
from the ground and at a horizontal distance
from particle 2. If a graph is plotted between
and
for the condition of collision of the two then (
on
-axis and
on
-axis
![](data:image/png;base64,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)
Two particles 1 and 2 are projected with same speed
as shown in figure. Particle 2 is on the ground and particle 1 is at a height
from the ground and at a horizontal distance
from particle 2. If a graph is plotted between
and
for the condition of collision of the two then (
on
-axis and
on
-axis
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATMAAACMCAMAAAAnbb54AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///wAAAObe3vf37zo6OsXFxWtrY62trRkZIVJSUhAICHNapaVazkJazqVahEJahGNaEBBCUnNazhBazhBahHNae0JKQq1aUqUpUmspUq1aGaUpGWspGYxaUqUIUmsIUoxaGaUIGWsIGYSUjErvnKWlGaUZpULvGaUZ70IZ70IZpd695nPvWhCtWnPvGRCtGXMZpXMZ7xAZ7xAZpXOlWhDvWnOlGRDvGXvvnHvv3nuU70rO3kLOWqWEWkrOnKWEGULOGRDOWnOEGRDOGYSEhDoQUhAQUubv7zpjGRBCGTE6GTEZKaVa70Ja76VapUJapWNaMRBjUnNa7xBa7xBapd73zjo6Sq3v3q2U7+8Qpe8ZEM4Qpc4ZEKWMlM7W1jEQCN73a973EBBjGe8Q5u9aEO/OEO+UEO+lnBmM7xmMrc4Q5s5aEM7OEM6UEM6lnBmMzhmMjBAZEKWllNbe3u8xpe8ZMe9zpe8pY85zpc4pY84xpc4ZMe9Spe8IY85Spc4IY973nHulpd73Qu/WnKXOa0qM70KMa0qMraXOKUKMKaUphKUpzkIpzkIphO+c5nPOaxCMa3POKRCMKXMphHMpzhApzhAphHvOrXvO73ulzs7WnKXOSkqMzkKMSkqMjKXOCEKMCKUIhKUIzkIIzkIIhM6c5nPOShCMSnPOCBCMCHMIhHMIzhAIzhAIhHvOjHvOznuEznOEUgAICO/Oc+9z5u9ac+8x5u9aMe/OMe+UMe+lve+Ucxmt7xmtrRnv7xnvrc7Oc85z5s5ac86UcxnO7xnOre/OUu9S5u9aUs4x5s5aMc7OMc6UMc6lve+UUhmtzhmtjBnvzhnvjM7OUs5S5s5aUs6UUhnOzhnOjHOEc63vra3O762lzq3vjK3Ozq2Ezq3FlK29taXva0rv7zpaWkLva0qt76Wla0Kta0qtraXvKUKtKaXvSkrvzkLvSkqtzqWlSkKtSkqtjKXvCEKtCObWxXuEpWtKWq2MrVpjWu/e9/fe3t73/wAAEP/v/wAAAPZgSZQAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAI7UlEQVR4Xu2dW5LiLBSAjeGWvCcb8NFtUEVV5z1v2msAduY+ZgE8UtVbSHmp0vohokZnxum0IRd/vrQJcRwj5HDOgRxgFggEAoFAIBAIBAKBQI/EjLlUn8T1ReeyPpkWUovtHrqT3pBYZTqezRhN8BA37CUOmoIoWrmzvpA7EKXKiNgBEVS5NydDhVemzIQ764u1vVH50lRQ8UV7F/JXYXKd8WjhzjpkjvXfVRXTIo8+bGHBFT6c35sUgqQ7l3QwCaU02uYVIErUTkP5F211opxoc4R4ikZghsnmTs7ipUBJQl/UzRIRTgjYCn34Y+nrgliNMNEyM3J2p890AnjESU5fys1Jl1GURhwke0Xx7zqr+vpcnGYQrl+U52EQ5NiUM51EZwoq5+xnzA8sZih1XxSRHAkM4bwpuXJPFkavTc4AnLmXM4lcRk2hocWK/mQT9bYl7nsMnPDCVPeG5B4SIuTyiZ0YNbumnMXQVKkL5NPoJLNddt891hvhVzlzcIJuYhUrnmE9n2TNnM0WTTljq4Z0bECZt6c8bwBs3Nec4aQAankrIxrlAk60yIzdTG9yJkWjzHI9lwf753bXw/NzB719E0/rqlmxRhnRNNEnl54asSCbppx9uHyanKKX3E3K3feQJFtgDR96AlalmKI3ewaTY6O9CXOXU5PXV7yNeGcKPyUgTxDVa/dmEzi9xvmNO302k+qqupNXHAH4xY2AGc+Mxac/a60JFxmjm0ixm2ZZZ67QAH5FQ0uqxN+bTpOGVSJPebKDt8xpwI2TAV7s2IoPjfvwZugsMSh9K6ClSvbUGjl3HnjgJKGGhkY3RkUzsR6ku3u6rKnCLhn4JmuKQpm1xJbZ26pvT6xpFuSsJUsjZ8ECtGOtgj5riwxy1hpIM/tEKNCCIGftqYJ/1hrrn021z3kogn/WHitnQZ+1AwZ91ppgN9tTGf8stNHbEexme0L/2XOYXFfyoR872M3nzH9R+hjQatqbQc6ewPSe5A9SFezmc5hUaf7QixH8s3+xIvu5SzqCnP0Dpnjmkhesf+aSgT8htzZ8OpaNwIpgN/8Bzks9O0CxuhnP4J/9AwrQUopFVqhrjFiQs+ew7ccCaqHpJoeXNuYw/tnZsZ6/OvylB+ZfROyEnGFe2qGBNf3bzZhJiOtravpr7NHvDIJPiten2Yqjq8fR//MAhreAJLawFP8a+ygLJsBxbxwLiVJ17f6x+qzfGsIwiKJPW1gYlI041VEisw1XS6PCSnIbWtf/8wBW0Y9jPczugOnYfcMqiQr7G0We3H7qAHbzxHaACCPc8/GPs8OE13Uy+7ADnR2DtDfXOacHc209H3sX8Y7nVoswYz1vnWiDtDcZ4lk1i8c/aECeG5sxLAA8XAVtmHgNdESMQfjQXzA+YN3YNGaLEyGvY5GG6ddQGyQlHP+gMY3qwYFMlGB3u8HDxGtkPMFwAvH1cFePOT1VC9GY5GKY9qYAQOkJDMNgrgfocjwzTLwGLsHKeIoTZRg5w1s19lbTE4Z5HgDxnwYsTgVrN/s3X2z0XsYzqvB8szWhn7Y9tsxcMvBNgpy1x7Y3R9+EGRnWbo7fHx8X1j8LctYOK2cuGfgm1j8LctaONd0HfdYSO4Y/yFk7rJy5ZOCb2HiNN/VpYylvffhd8r528wQFpaIxzU9nDBdPK6HPB8KxXCQFKUC+6v4qQzx3spFBWlDl8yGhvEy7+NF9ofXdfxbPGIMiywlPS58XxuQywWTR+WX67deIl5qqbVLaiQzT16YRfk5jMrwIdT2TcG9zLNn6iIXKL3Nlpluft+o6V7Eh7zqDxj8Tbj5jr0hNE9CcxpYoGbPY/WvnCOAuYwC7ju/OUhVFnvjfQEHuZ/3lxE5f54vi6C5jeBx68zIS7+2MvL4pwONEySknhZG7wsdGSHGZ+tWAOo8LYewg3by8/mCVpnvCm+VGtlhjg9l1/6eFuhYa73stk+5gEO6E0WkuJ1H6VVnPw2ynjvdmF59g5gqN979mTrdY1yzJjXNmMyN8tgNmUBUk2hCQTbzIDCfTCMCrxKg3Xv5y7/lBYpUkaJorY/zO2VXLGnPle4Etodcm7QD4baMHAoH/IV56f98bKKbvv/QNHv3QtvGxA9Sl3hBPagcD2vfjgP6APp462dENHpaWHAmSrryUGS7p2xpOmdRDuDtHvLE+q/LEl5y9bViQkTMv4xAG0meMSWny49ehhoknOQN+9ORzThDZqADmt2vDl5wN4p8xnQCwpZQ2R0V2z9KbnC36lzOG0gTaWbIWXuWs8qbPBpCzKk/tVRfol1f7s/YlZw/+WcwgFtjzynNyXy8pKJuLc72IxEI8LpjXh900xmypBSqO9ZwSHjnRI++4yQYzYhdmrOThZov92c2LfxZLTfcgJySKkF8xM7Um23x2W2gxJhEnoEzQLbTRn920fUHSVEiKknNIBX9pKc7vsd5HoNsYLqbcry+3aoW1rfVzf3ImpamQgB9TFxlAqJwf5kzOO97uZmCGZePWMNb83I82NseX8KmNjZ+x1dTUTS9yhglI8rJ+sH2BJwoZMqQ6fSF6lwFByNVia/r65dD2tjayyYOtpgnxo2R0Y+XqCzw126bTF0+PEXByVdUKx9jO7cU7EwWPOD9y87H68z9Ip5w0wqfO8MhT3eSfd6F0hrQo87IEeQnq3fnvpWN9KJArIlpXSrjdXKTghI2oA/OZ8wfvkt993+ybdSXinwQQ7ieWEgNl4wDyxgUJteuaVo2X3f3k6F6Xs3MGWFJPfoYBubZAmLz/P3cnjeTdSSNZ78VtDe6IF3uKIc499Z/ZZyjGj10plICztHHlcylzhlVGqcryvOMYZFrUvz4COcpMgZkvZ57s5q2NfoDGetYhnKnqzD3/HaYh04iQXHRq004aGJVYkNxYzMu98NcOuFqvk60iWuyL19ZK/wexEeLYVqduRUCqz6NdoN20n6433LTRvciZLh/6HE09pX6j6bxwwAtRz7vVwJecwceFK94IX/1n8fsuBu+t/+ydWXt67vTOHJQKctaSeOn1cUMg8BNms/8AvMzOFWHMtrcAAAAASUVORK5CYII=)
Physics-General
physics-
a) Name the experiment for which the adjacent graph, showing the variation of intensity of scattered electrons with the angle of scatter ing (q) was obtained.
b) Also name the important hypothesis that was confirmed by this experiment
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458425/1/937176/Picture64.png)
a) Name the experiment for which the adjacent graph, showing the variation of intensity of scattered electrons with the angle of scatter ing (q) was obtained.
b) Also name the important hypothesis that was confirmed by this experiment
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458425/1/937176/Picture64.png)
physics-General
physics-
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is
, then the ratio of tensions in the three sections of the string is
![](data:image/png;base64,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)
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is
, then the ratio of tensions in the three sections of the string is
![](data:image/png;base64,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)
physics-General
physics-
A ball of mass
kg is attached to the end of a string having length
0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is
![](data:image/png;base64,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)
A ball of mass
kg is attached to the end of a string having length
0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is
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physics-General
maths-
The ellipse
and the straight line y = mx + c intersect in real points only if
The ellipse
and the straight line y = mx + c intersect in real points only if
maths-General