Physics

When the arrow is released, the elastic potential energy stored in the stretched bow is converted into the kinetic energy of the moving arrow.

The band theory of solids explains the electronic properties of all types of materials: electrical insulators, conductors, and semiconductors. It describes how the energy bands and band gaps determine whether a material conducts electricity or not, thus satisfactorily explaining all these categories.

Work and torque both have the same dimensional formula, which is M L^2 T^-2. This is because work is force times distance and torque is force times lever arm distance, so their dimensions match.

When a wire is stretched within its elastic limit, it behaves like a spring obeying Hooke’s law. The work done (and hence elastic potential energy stored) is equal to the area under the force-extension graph, which is (1/2)Fx.

An n-type semiconductor is doped with donor atoms that add extra electrons, which are negatively charged. However, the material as a whole remains electrically neutral because the number of positive charges (protons in the lattice) balances the number of negative charges (electrons). Thus, the net charge on n-type material is neutral.

The valence electrons occupy the valence band, which is the highest range of electron energies where electrons are normally present at absolute zero temperature. The conduction band is above the valence band and is typically unoccupied unless electrons gain enough energy.

Energy consumed is power multiplied by time. For a 60 watt bulb running for 2 seconds, energy = 60 W × 2 s = 120 joules. However, the options given are 120 J (A), 60 J (B), 30 J (C), and 0.02 J (D). The correct calculation yields 120 J, which corresponds to option A, not C. Therefore, the correct answer is A.

A magnetometer is an instrument specifically designed to detect and measure very weak magnetic fields, making it the correct choice. Squids are animals, MRI is a medical imaging technique that uses magnetic fields but does not detect weak fields externally, and an oscilloscope measures electrical signals, not magnetic fields.

Average power equals instantaneous power when work is done at a uniform rate because power is the rate of doing work. If the rate is constant, the instantaneous power at any moment matches the average power over the time interval.

Materials where valence electrons are tightly bound to their atoms at low temperatures do not allow free movement of electrons, making them insulators. This restricts electrical conductivity, distinguishing them from conductors and semiconductors.