HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Physics

When two cells of emf's E₁ and E₂ are connected in series so as to assist each other, their balancing length on a potentiometer wire is found to be 2.7 m. When the cells are connected in series so as to oppose each other, the balancing length is found to be 0.3 m. Compare the emf's of the two cells.

The emf of a cell is balanced by a length of 120 cm of a potentiometer wire. When the cell is shunted by a resistance of 10 Ω, the balancing length is reduced by 20 cm. Find the internal resistance of the cell.

A piece of straight wire has mass 20 g and length 1 m. It is to be levitated using a current of 1 A flowing through it and a perpendicular magnetic field B in a horizontal direction. What must be the magnitude B of the magnetic field?

An aircraft of wing span of 50 m flies horizontally in the Earth's magnetic field of 6 x 10^-5 T at a speed of 400 m/s. Calculate the emf generated between the tips of the wings of the aircraft.

A metal disc of radius 30 cm spins at 20 revolution per second about its transverse symmetry axis in a uniform magnetic field of 0.20 T. The field is parallel to the axis of rotation. Calculate
(a) the area swept out per second by the radius of the disc
(b) the flux cut per second by a radius of the disc
(c) the induced emf between the axle and rim of the disc.

The primary and secondary coils of a transformer each have an inductance of 200 x 10^-6 H. The mutual inductance between the windings is 4 x 10^-6 H. What percentage of the flux from one coil reaches the other?

A circular coil of 100 turns with a cross-sectional area of 1 m² is kept with its plane perpendicular to the magnetic field of 1 T. The magnetic flux linkage is ______.

Explain what you understand by the de Broglie wavelength of an electron. Will an electron at rest have an associated de Broglie wavelength? Justify your answer.

The de Broglie wavelengths associated with an electron and a proton are the same. What will be the ratio of

1. their momenta
2. their kinetic energies?

Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an α-particle, what are the possibilities for the other particle?

Find the ratio of the de Broglie wavelengths of an electron and a proton when both are moving with the (a) same speed, (b) the same kinetic energy, and (c) the same momentum. State which of the two will have a longer wavelength in each case.

What is the amount of \[\ce{_27^60Co}\] necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years?

Disintegration rate of a sample is 10¹⁰ per hour at 20 hours from the start. It reduces to 6.3 x 10⁹ per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.

The isotope \[\ce{^57Co}\] decays by electron capture to \[\ce{^57Fe}\] with a half-life of 272 d. The \[\ce{^57Fe}\] nucleus is produced in an excited state, and it almost instantaneously emits gamma rays.
(a) Find the mean lifetime and decay constant for ⁵⁷Co.
(b) If the activity of a radiation source ⁵⁷Co is 2.0 µCi now, how many ⁵⁷Co nuclei does the source contain?

c) What will be the activity after one year?

A source contains two species of phosphorous nuclei, \[\ce{_15^32P}\] (T_1/2 = 14.3 d) and \[\ce{_15^33P}\] (T_1/2 = 25.3 d). At time t = 0, 90% of the decays are from \[\ce{_15^32P}\]. How much time has to elapse for only 15% of the decays to be from \[\ce{_15^32P}\]?

Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of ¹⁴C averaged about 0.255 Bq per gram of carbon.
(a) What fraction of carbon atoms were ¹⁴C?
(b) An archaeological specimen containing 500 mg of carbon, shows 174 decays in one hour. What is the age of the specimen, assuming that its activity per unit mass of carbon when the specimen died was equal to the average value of the air? The half-life of ¹⁴C is 5730 years.

A cyclist riding a bicycle at a speed of `14sqrt3` m/s takes a turn around a circular road of radius `20sqrt3` m without skidding. Given g = 9.8 m/s², what is his inclination to the vertical ______.

A string of length ℓ fixed at one end carries a mass m at the other. The string makes 2/π revolutions/sec around the vertical axis through the fixed end. The tension in the string is ______.

Find the radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center.

State and explain the theorem of parallel axes.