1
IIT-JEE 2008 Paper 2 Offline
+3
-1

A bob of mass M 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 $$\theta$$ at which the speed of the bob is half of that at A, satisfies,

A
$$\theta = {\pi \over 4}$$
B
$${\pi \over 4} < \theta < {\pi \over 2}$$
C
$${\pi \over 2} < \theta < {{3\pi } \over 4}$$
D
$${{3\pi } \over 4} < \theta < \pi$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in 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,

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
3
IIT-JEE 2008 Paper 2 Offline
+3
-1

A vibrating string of certain length 1 under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is:

A
344
B
336
C
117.3
D
109.3
4
IIT-JEE 2008 Paper 2 Offline
+3
-1

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is $$\frac{d}{3}$$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is:

A
$${{6{\varepsilon _0}R} \over {5d + 3Vt}}$$
B
$${{(15d + 9Vt){\varepsilon _0}R} \over {2{d^2} - 3dVt - 9{V^2}{t^2}}}$$
C
$${{6{\varepsilon _0}R} \over {5d - 3Vt}}$$
D
$${{(15d - 9Vt){\varepsilon _0}R} \over {2{d^2} + 3dVt - 9{V^2}{t^2}}}$$
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