Magnetism and Matter — Physics STD 12 Science — Question

²³⁸U decays to ²⁰⁶Pb with a half-life of 4.47 × 10⁹y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00mg of ²³⁸U and 0.600mg of ²⁰⁶Pb. Assuming that all the lead has come from uranium, find the life of the rock.

A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes a time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will:

1. Take a time longer than T to slide down the wedge.
2. Take a time shorter than T to slide down the wedge.
3. Remain at the top of the wedge.
4. Jump off the wedge.

A charged particle of charge e and mass m is moving in an electric field E and magnetic field B. Construct dimensionless quantities and quantities of dimension [T]^-1.

A block of mass 2.0kg moving at 2.0m/s collides head on with another block of equal mass kept at rest.

1. Find the maximum possible loss in kinetic energy due to the collision.
2. If the actual loss in kinetic energy is half of this maximum, find the coefficient of restitution.

During a thunderstorm the ‘live' wire of the transmission line fell down on the ground. A group of boys passing through noticed it and some of them wanted to place the wire by the side. As they were approaching the wire and trying to lift it, Bari noticed it and immediately pushed them away to prevent them from touching the wire. Two of them got hunt in the process. Bari took them to a doctor to get medical aid.
Based on the above paragraph, answer the following:

1. Write two values which Bari displayed during the incident.
2. Why is it that a bird can sit over a suspended ‘live' wire without any harm whereas touching it on the ground can give a fatal shock?
3. The electric power from a power plant is set up to a very high voltage before transmitting it to distant consumers. Write the reason for it.

A proton projected in a magnetic field of 0.020T travels along a helical path of radius 5.0cm and pitch 20cm. Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton = 1.6 × 10^-27kg

An adiabatic vessel of total volume V is divided into two equal parts by a conducting separator. The separator is fixed in this position. The part on the left contains one mole of an ideal gas (U = 1.5nRT) and the part on the right contains two moles of the same gas. Initially, the pressure on each side is p. The system is left for sufficient time so that a steady state is reached. Find,

1. The work done by the gas in the left part during the process.
2. The temperature on the two sides in the beginning.
3. The final common temperature reached by the gases.
4. The heat given to the gas in the right part.
5. The increase in the internal energy of the gas in the left part.

A tuning fork of unknown frequency makes 5 beats per second with another tuning fork which can cause a closed organ pipe of length 40cm to vibrate in its fundamental mode. The beat frequency decreases when the first tuning fork is slightly loaded with wax. Find its original frequency. The speed of sound in air is 320m/s.