Question
Figure shows a glowing mercury tube. The illuminances at point A, B and C are related as
![](data:image/png;base64,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)
The correct answer is: ![B equals C less than A](data:image/png;base64,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)
By the symmetry of the rays and location of the points.
Related Questions to study
A block rests on a rough inclined plane making an angle
of with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : ![open parentheses text taken end text g equals 10 ms squared close parentheses](data:image/png;base64,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)
A block rests on a rough inclined plane making an angle
of with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : ![open parentheses text taken end text g equals 10 ms squared close parentheses](data:image/png;base64,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)
In
then the triangle is.
In
then the triangle is.
Two masses
tied to a string are hanging over a light friction less pulley. What is the acceleration of the masses when they are free to move ? (g=9.8
)
![](data:image/png;base64,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)
Two masses
tied to a string are hanging over a light friction less pulley. What is the acceleration of the masses when they are free to move ? (g=9.8
)
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)
A machine gun fires a bullet of mass 40 g with a velocity 1200 . The man holding it, can exert maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
A machine gun fires a bullet of mass 40 g with a velocity 1200 . The man holding it, can exert maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ) can a man of 60 kg climb on the rope
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ) can a man of 60 kg climb on the rope
Three identical blocks of masses m = 2 kg are drawn by a force F with an acceleration of 0.6 ms–2 on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C
Three identical blocks of masses m = 2 kg are drawn by a force F with an acceleration of 0.6 ms–2 on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C
When forces are acting on a particle of mass m such that and are mutually perpendicular, then the particle remains stationary. If the force is now removed then the acceleration of the particle is-
When forces are acting on a particle of mass m such that and are mutually perpendicular, then the particle remains stationary. If the force is now removed then the acceleration of the particle is-
In above problem, the value(s) of F for which M and m are stationary with respect to![straight M subscript 0](data:image/png;base64,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)
In above problem, the value(s) of F for which M and m are stationary with respect to![straight M subscript 0](data:image/png;base64,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)
Consider a special situation in which both the faces of the block are smooth, as shown in adjoining figure. Mark out the correct statement(s)
Consider a special situation in which both the faces of the block are smooth, as shown in adjoining figure. Mark out the correct statement(s)
Imagine a situation in which the horizontal surface of block is smooth and its vertical surface is rough with a coefficient of friction
In above problem, choose the correct value(s) of F which the blocks M and m remain stationary with respect to M0
Imagine a situation in which the horizontal surface of block is smooth and its vertical surface is rough with a coefficient of friction
In above problem, choose the correct value(s) of F which the blocks M and m remain stationary with respect to M0
Imagine a situation in which the horizontal surface of block is smooth and its vertical surface is rough with a coefficient of friction Identify
the correct statement(s)
Imagine a situation in which the horizontal surface of block is smooth and its vertical surface is rough with a coefficient of friction Identify
the correct statement(s)
A solid sphere of mass 10 kg is placed over two smooth inclined planes as shown in figure. Normal reaction at 1 and 2 will be ![open parentheses g equals 10 ms to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
A solid sphere of mass 10 kg is placed over two smooth inclined planes as shown in figure. Normal reaction at 1 and 2 will be ![open parentheses g equals 10 ms to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
The number of integral values of k for which the equation has a solution is
The number of integral values of k for which the equation has a solution is