1. A charge + q is fixed at each of the points x = x0, x = 3x0, x = 5x0 ….∞ on the x-axis and a charge – q is fixed at each of the points x = 2x0, x = 4x0, x = 6x0 …. ∞. Here x0 is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be Q/4πε0r.
Then the potential at the origin due to the above system of charges is :
(A) 0 (B) q / (8πε0x0 (ln 2))
(C) (q (ln 2))/(4πε0x0) (D) ∞
2. Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to :
(A) I (B) I sin²θ..
(C) I cos²θ (D) I cos²(θ/2)
3. A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement (s) from the following :
(A) the entire rod is at the same electric potential
(B) there is an electric field in the rod
(C) the electric potential is highest at the centre of the rod and decreases towards its ends.
(D) the electric potential is lowest at the centre of the rod and increases towards its ends.
4. A positively charged thin metal ring of radius R is fixed in the xy plane with its centre at the origin O. A negatively charged particle P is released from rest at the point (0, 0, z0) where z0 < 0. Then the motion of P is :
(A) period for all values of z0 satisfying 0 < z0 < ∞
(B) simple harmonic for all values of z0 satisfying 0 < z0 < R
(C) approximately simple harmonic provided z0 < < R
(D) such that P crosses 0 and continues to move along the negative z-axis towards z = – ∞.
5. A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let 0 be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be:
(A) real and will remain at C
(B) real and located at a point between C and ∞
(C) virtual and located at a point between C and 0
(D) real and located at a point between C and 0
Source: 1998 JEE paper