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

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.

The maximum speed of a particle executing S.H.M. is 10 m/s and maximum acceleration is 31.4 m/s². Its periodic time is ______ 

A simple pendulum is inside a spacecraft. What will be its periodic time? 

What is Solenoid?

What is Toroid?

A solenoid of length 50 cm of the inner radius of 1 cm and is made up of 500 turns of copper wire for a current of 5 A in it. What will be the magnitude of the magnetic field inside the solenoid? 

Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid Why?

A toroid of 4000 turns has an outer radius of 26 cm and an inner radius of 25 cm. If the current in the wire is 10 A. Calculate the magnetic field of the toroid. 

A solenoid of length π m and 5 cm in diameter has a winding of 1000 turns and carries a current of 5 A. Calculate the magnetic field at its centre along the radius.

Using Ampere's Law, derive an expression for the magnetic induction inside an ideal solenoid carrying a steady current.

Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λN_O e^-λt.  

Obtain an expression for magnetic induction of a toroid of ‘N’ turns about an axis passing through its centre and perpendicular to its plane.

A conducting rod along the equator is 1 m long and carries a current of 15 A from east to west. The magnitude of Earth's magnetic field at the equator is `4/3 xx 10^(-4)` T. The magnitude and direction of the force on the rod are ______.

Why does hot soap water help to remove tough stains on a fabric?

The half-life of `""_82^210Pb` is 22.3 y. How long will it take for its activity 0 30% of the initial activity?

For a solenoid and a toroid, the number of turns per unit length is n and the respective interior volume is V. The self inductance is proportional to n² and V for ______.

A current of 10 A passes through a coil having 5 turns and produces magnetic field at the centre of the coil having magnitude 0.5 x 10^-4 T. Calculate diameter of the coil.

(µ₀ = 4π x 10^-7 Wb/Am)