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1. A rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact.
2. An observer standing on a railway crossing receives frequencies of 2.2 kHz and 1.8 kHz when the train approaches and recedes from the observer. Find the velocity of the train. [the speed of the sound in air is 300 m/s].
3. A U-shaped tube contains a liquid of density r and it is rotated about the line as shown in the figure. Find the difference in the levels of liquid column.
4. A conducting bubble of radius a, thickness t (t < < a) has potential V. Now the bubble collapses into a droplet. Find the potential of the droplet.
5. The potential energy of a particle varies as
U (x) = E0 0 < x < 1
= 0 x > 1
For 0 < x < 1. de Broglie wavelength is l1 and for x > 1 the de Broglie wavelength isl2. Total energy of the particle is 2E0. Find l1/l2 .
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