1. A whistling train approaches a junction. An observer standing at junction observes the frequency to be 2.2 KHz and 1.8 KHz of the approaching and the receding train. Find the speed of the train (speed of sound = 300 m/s)
2. A conducting liquid bubble of radius a and thickness t (t <
3. The potential energy of a particle of mass m is given by
V (x) = E0 when 0 is l.t. or = x is l.t. or = 1
V (x) = 0 when x>1
λ1 and λ2 are the de−Broglie wavelengths of the particle, when 0 ≤ x ≤ 1 and x > 1 respectively. If the total energy of particle is 2E0, find λ1/λ2.
4. A U tube is rotated about one of it’s limbs
with an angular velocity ω. Find the difference
in height H of the liquid (density ρ) level,
where diameter of the tube d << L.
5. The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale. Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.
Source 2005 JEE Mains