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

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.

The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______ 

The power radiated by a perfect blackbody depends only on its ______ 

Calculate the value of λ_max for radiation from a body having a surface temperature of 3000 K. (b = 2.897 x 10-3 m K) 

Calculate the energy radiated in one minute by a blackbody of surface area 200 cm² at 127 °C (σ = 5.7 x 10^-8 J m^-2 s^-1 K^-4)  

Under which condition laws of Boyle, Charles, and Gay-Lussac are valid?

On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident? 

Why the temperature of all bodies remains constant at room temperature?

Above what temperature, all bodies radiate electromagnetic radiation? 

If the density of nitrogen is 1.25 kg/m³ at a pressure of 10⁵ Pa, find the root mean square velocity of nitrogen molecules. 

Compare the rate of radiation of metal bodies at 727 °C and 227 °C.  

A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature. 

A particle is performing simple harmonic motion with amplitude A and angular velocity ω. The ratio of maximum velocity to maximum acceleration is ______.