IIT-JEE-2008-Physics-Paper2

PAPER - II

1.     Consider a system of three charges q/3, q/3, -2q/3  and  placed at points A, B and C respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60^o

        Figure :

(A)    The electric field at point O is  directed along the negative x-axis

(B)    The potential energy of the system is zero

(C)    The magnitude of the force between the charges at c and B is .

(D)    The potential at point O is

2.     A radioactive sample S1 having an activity of 5µCi has a twice the number of nuclei as another sample S2 which has an acitivity of 10mCi. The half lives of S1 and S2 can be

        (A)    20 years and 5 years, respectively

        (B)    20 years and 10 years, respectively

        (C)    10 years each

        (D)    5 years each

3.     Transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is

        Figure :

        (A) (√3 π )/50 j ̂ m/s

        (B) -(√3 π )/50 j ̂ m/s

        (C) (√3 π )/50 i ̂ m/s

        (D) -(√3 π )/50 i ̂ m/s

4.     A block (B) is attached to two unstretched springs S1 and S2 with spring constant k and 4 k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio x/y  is

               Figure:

        (A)    4

        (B)    2

        (C)   1/2

        (D)   1/4

5. is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle q is which the speed of the bob is half of that at A, satisfies

        Figure:

        (A)    q = π/4

        (B)    π/4  < q < π/2

        (C)    π/2 < q < 3π/4

        (D)    3π/4 < q < π

6.     A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has 
sub-hemispherical soap bubble as shown in figure. Just after opening the valve

        Figure :

(A)    air from end 1 flows towards end 2. No change in the volume of the soap bubbles

(B)    air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases

(C)    no change occurs

(D)    air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases

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