Iit jee 2007 physics solutions

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In an experiment to determine the focal length(f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P.The student looks at the pin and its inverted image from a distance keeping hi

In an experiment to determine the focal length(f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P.The student looks at the pin and its inverted image from a distance keeping his eye in the line with PA.When the student shifts his eye towards left, the image appears to the right of the object pin. Then 

Solution:

Since the image appears to the right of the object when the student shifts his eye towards the left, the image is nearer to the student and hence the image distance ‘v’ is greater than the object distance ‘u’. This is possible only if the object is placed between f and 2f. So the correct answer is

f < x < 2f



28th February 2019

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A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius.. Both the cylinders are initially electrically neutral.

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius.. Both the cylinders are initially electrically neutral.
 
(a) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
(b) A potential difference appears between the two cylinders when a charge density is given to the outer cylinders.
(c) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders
(d) No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
Solution:
When the outer cylinder is charged, E = 0 inside the cylinder.
                                 r2
Hence, V2 - V1 = - ∫ E.dr = 0
                              r1
When the inner cylinder is charged, there exists an electrified in the outer side and thus leads to potential difference. If λ is the charge per unit length , the electric field at a r from the axis of cylinder is
Er = (λ/2πε)r^/r


                    r2
V2 - V1 =  - ∫ E.dr
                r1
           = (λ/2πε) ln(r2/r1)
Choosing V1 = 0 at r = r1, the potential at the outer cylinder will be
V = (λ/2πε)ln(r1/r2)
Thus option a is correct.

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