HSC Science (Electronics) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

The periodic time of a linear harmonic oscillator is 2π second, with maximum displacement of 1 cm. If the particle starts from extreme position, find the displacement of the particle after π/3  seconds.

State the law of radioactive decay.

A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x10⁸ N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x10¹⁰ N/m².

Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus

Represent Radioactive Decay curve using relation `N = N_o e^(-lambdat)` graphically

Answer in brief:

Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?

The specific heat capacity of water is 

The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.

A body of mass 1 kg is mafe to oscillate on a spring of force constant 16 N/m. Calculate (a) Angular frequency, (b) Frequency of vibrations.

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

The period of oscillation of a body of mass m₁ suspended from a light spring is T. When a body of mass m₂ is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m₁ and m₂

A 20 cm wide thin circular disc of mass 200 g is suspended to rigid support from a thin metallic string. By holding the rim of the disc, the string is twisted through 60° and released. It now performs angular oscillations of period 1 second. Calculate the maximum restoring torque generated in the string under undamped conditions. (π³ ≈ 31)

Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10^-5 Wb/m². The magnet has a moment of inertia 3 × 10^-6 kg/m² and magnetic moment 3 A m².

A toroid of a central radius of 10 cm has windings of 1000 turns. For a magnetic field of 5 × 10^-2 T along its central axis, what current is required to be passed through its windings?

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.

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 ______