Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Physics

The variation of decay rate of two radioactive samples A and B with time is shown in figure.

Which of the following statements are true?

1. Decay constant of A is greater than that of B, hence A always decays faster than B.
2. Decay constant of B is greater than that of A but its decay rate is always smaller than that of A.
3. Decay constant of A is greater than that of B but it does not always decay faster than B.
4. Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant.

Draw a graph showing the variation of decay rate with number of active nuclei.

Which sample, A or B shown in figure has shorter mean-life?

Consider a radioactive nucleus A which decays to a stable nucleus C through the following sequence:

A→B→C

Here B is an intermediate nuclei which is also radioactive. Considering that there are N₀ atoms of A initially, plot the graph showing the variation of number of atoms of A and B versus time.

A piece of wood from the ruins of an ancient building was found to have a ¹⁴C activity of 12 disintegrations per minute per gram of its carbon content. The ¹⁴C activity of the living wood is 16 disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of ¹⁴C is 5760 years.

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is :

\[\ce{^38Sulphur ->[half-life][= 2.48h] ^{38}Cl ->[half-life][= 0.62h] ^38Air (stable)}\]

Assume that we start with 1000 ³⁸S nuclei at time t = 0. The number of ³⁸Cl is of count zero at t = 0 and will again be zero at t = ∞ . At what value of t, would the number of counts be a maximum?

The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

1. Plot the graph of R versus t and calculate the half-life from the graph.
2. Plot the graph of ln `(R/R_0)` versus t and obtain the value of half-life from the graph.

What can be the causes of helical motion of a charged particle?

The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.

The Earth's magnetic field at the Equator is approximately 0.4 G. Estimate the Earth's magnetic dipole moment. Given : Radius of the Earth = 6400 km.

Write the truth table for the combination of the gates shown. Name the gates used.

Identify the logic gates marked 'P' and 'Q' in the given circuit. Write the truth table for the combination.

You are given the two circuits as shown in following figure. Show that circuit

1. acts as OR gate while the circuit
2. acts as AND gate.

(a)

(b)

Write the truth table for a NAND gate connected as given in the following figure.

Hence identify the exact logic operation carried out by this circuit

You are given two circuits as shown in following figure, which consist of NAND gates. Identify the logic operation carried out by the two circuits.

(a)

(b)

Write the truth table for circuit given in figure below consisting of NOR gates and identify the logic operation (OR, AND, NOT) which this circuit is performing.

(Hint: A = 0, B = 1 then A and B inputs of second NOR gate will be 0 and hence Y=1. Similarly work out the values of Y for other combinations of A and B. Compare with the truth table of OR, AND, NOT gates and find the correct one.)

Write the truth table for the circuits given in following figure consisting of NOR gates only. Identify the logic operations (OR, AND, NOT) performed by the two circuits.

(a)

(b)

An iron ring of relative permeability µ_r has windings of insulated copper wire of n turns per meter. When the current in the windings is I, find the expression for the magnetic field in the ring.

Give the truth table and circuit symbol for NAND gate

Draw logic symbol of an OR gate and write its truth table.