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A particle of mass m moves in circular orbits with potential energy V( ) = , where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle’s orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the nth orbit (here h is the Planck’s constant)

Answer: b, c P.E., V(r) = Fr Therefore, Force = -dV/dr = – F F = mv2 / R …. (1) MvR = nh / 2 π ….. (2) From (2)... View Article

An open-ended U-tube of uniform cross-sectional area contains water (density 103kg m−3). Initially, the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg m−3 is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio h2 / h2 of the heights of the liquid in the two arms is

a) 15 / 14 b) 35 / 33 c) 7 / 6 d) 5 / 4 Answer: b ∵ Pressure will be same at same horizontal level, PA = PB (Same horizontal level)... View Article

A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge Q through a switch. The coil is in a horizontal uniform magnetic field Bo parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)

a) /2 2 b) 2 c) 2 2 d) 4 2 Answer: b After closing switch, within a fraction of seconds, entire charge flows through the coil... View Article

A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)

Answer: b ∵ In this case pure rolling without slipping, Let radius of roller is R and radius of axle is r. ∵ As we know, v = ω r... View Article