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```IIT JEE 2009 Physics Paper2 Code 1 Solutions

3.     A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can slide 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 x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stays at rest with respect to the wire, from the y-axis is

(A) a/gk

(B) a/2gk

(C) 2a/gk

(D) a/4gk

Sol.   (B)

tan θ = a/g

tan θ = dy/dx = 2kx

Hence,=> x = a/2gk

4.     The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

(A) (k1 A)/k2

(B) (k1 A)/k1

(C) (k1 A)/(k1 + k2 )

(D) (k2 A)/(k1 + k2 )

Sol.   (D)

We have,

x1 + x2 = A

k1x1 = k2x2

Hence x1 = (k2 A)/(k1 + k2 )

MULTIPLE CORRECT CHOICE TYPE

5.     Under the influence of the coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s).

(A)    The angular momentum of the charge -q is constant

(B)    The linear momentum of the charge -q is constant

(C)    The angular velocity of the charge -q is constant

(D)    The linear speed of the charge -q is constant

Sol.   (A)    The angular momentum of the charge -q is constant

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