Physics-
General
Easy
Question
In the given figure, what is the angle of prism
![](data:image/png;base64,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)
- A
- B
- C
- D
The correct answer is: C
Angle of prism is the angle between incident and emergent surfaces.
Related Questions to study
physics-
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P as shown in the figure. The ray will suffer
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)
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P as shown in the figure. The ray will suffer
![](data:image/png;base64,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)
physics-General
Physics-
A bob of mass
is suspended by a massless string of length
. The horizontal velocity
at position
is just sufficient to make it reach the point
. The angle
at which the speed of the bob is half of that at
, satisfies
![](data:image/png;base64,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)
A bob of mass
is suspended by a massless string of length
. The horizontal velocity
at position
is just sufficient to make it reach the point
. The angle
at which the speed of the bob is half of that at
, satisfies
![](data:image/png;base64,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)
Physics-General
maths-
The foot of the perpendicular on the line drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is
The foot of the perpendicular on the line drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is
maths-General
maths-
(where a, b are integers) =
(where a, b are integers) =
maths-General
maths-
maths-General
maths-
is equal to
is equal to
maths-General
maths-
Let denotes greatest integer function, then is equal to
Let denotes greatest integer function, then is equal to
maths-General
maths-
The value of is equal to
The value of is equal to
maths-General
Maths-
The value of
(where {x} is the fractional part of x) is
The value of
(where {x} is the fractional part of x) is
Maths-General
Maths-
The shortest distance between the two straight line
and
is
The shortest distance between the two straight line
and
is
Maths-General
physics-
A bob of mass M is suspended by a massless string of length L. The horizontal velocity at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
A bob of mass M is suspended by a massless string of length L. The horizontal velocity at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
physics-General
Physics-
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
Physics-General
physics-
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](data:image/png;base64,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)
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](data:image/png;base64,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)
physics-General
maths-
The equation of the plane containing the line
where al + bm + cn is equal to
The equation of the plane containing the line
where al + bm + cn is equal to
maths-General
physics-
A small body of mass
slides down from the top of a hemisphere of radius
. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
![](data:image/png;base64,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)
A small body of mass
slides down from the top of a hemisphere of radius
. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
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043rQ3+Isac9k4bZ/hSQZl5TRHj9ZP/P7wjvCLgQS6mlWL//wKY8xnfkzSc5NFneGB/ptBUvNdej2V9uwxiS5LOod5sadJaSnV1hZWXVEKP0nGMSNlneFA4tdLWfdlg2RGYWt1PWD9aJa0eYdV4VU9t/sA1uUN3fj1FXs/v/V6pe7KJrFW1zNW1gKv2NzCusWjq1lgtvI62+r1FXs/v/U6zd2XNpnOsU4vs4XnivzB1ia2hK/FHtnc6v+Uut+7dn+7UJV4mYHOqD+ztK4p7Bs4SP1de37eZhm13nU51GKd9qy6Goyd/qfTbHb3NJv9fFqP80vg2mFh1eIp3evwUCVeBhPsDhNV4mVqmc4RyGhXnlXiZbBIh4kq8QvKGZf+PPLcnNaY3u/PI8+i3esH/tmASvTn+8/77OJjix1FOot05TqdTqfT+RqXy39zjOnVHrSANQAAAABJRU5ErkJggg==)
physics-General