Note:
(i) All questions are compulsory. The marks allotted for each question are indicated against each question.
(ii) Write your name enrolment number, AI name, and subject on the top of the first page of the answer sheet.
1. Answer any one of the following questions in about 4060 words.
a) Two vector quantities are represented by :
r= r_{x}i + r_{y}j
F = F_{x}i +F_{y}j
Write the scalar, and vector products of these quantities. Give the names of two physical quantities which are obtained as the scalar product and vector product of two vector quantities.
Answer
b) Displacement of a simple harmonic oscillatoris expressed by the following equation. Y = 10^{2}sin (314t + π/4)
Where all the quantities are taken is SI units. Find the following characteristics of its oscillations.
Answer:
2. Answer any one of the following questions in about 4060 words
a) The positiontime graph of a particle moving in a straight line is given in the figure shown alongside. Calculate the average speed and average velocity of the particle.
Answer
by putting the values you can easily get the answer.
b) The distance of the image formed by anequiconvex lens, in air, from its second focus, x_{2}=30 cm, while the distance of the object from the first focus is, x_{1}= 10 cm. calculate the focal length of the lens.
Answer–
3. Answer any one of the following questions in about 4060 words
a) A long aluminum channel is bent in the form shown in the figure. What is the minimum height from which a marble should be rolled down in the channel so that is may negotiate the full loop and come out from the other side.
Answer–
To determine the minimum height from which a marble should
be rolled down in the channel so that it can negotiate the full loop, we can use the conservation of energy.
The potential energy at the initial height is converted into kinetic energy as the marble moves downward and then into both kinetic and potential energy as it moves around the loop. At the minimum height, all the initial potential energy should be converted into kinetic energy.
Now, to ensure that the marble negotiates the full loop, the centripetal force at the top of the loop must provide the necessary centripetal acceleration. At the top of the loop, the centripetal force is the gravitational force:
b) The magnifying power of an astronomical telescope is 100. In its normal adjustment the distance between the centres of the objective and eye piece of the telescope is 8.08 m. calculate the values of focal lengths of the objective and eye piece of the telescope.
Answer– With a magnifying power of 100 and a total telescope length
of 8.08 m, the focal length of the objective is 8 m, and the eyepiece’s focal
length is 0.08 m. These values enable optimal performance for astronomical
observations, ensuring a clear and detailed view of celestial objects through
the telescope.
4. Answer anyone of the following questions in 100150 words.
a) In Physics books you might have noticed the mass of earth to be 5.97×10 24 kg. Suggest a method by which the scientists find out the mass of earth.
Answer– Scientists determine the mass of the Earth using Newton’s law
of gravitation. One method involves measuring the gravitational force between
the Earth and a known mass (like a satellite) using the formula
where
G is the gravitational constant, M is the mass of the Earth, m is the mass of
the known object, and r is the separation between their centers. By rearranging
the formula, scientists can solve for M, the mass of the Earth.
b) Why do we have to modulate signals for effective wireless telecommunication? Give any three reasons. What do we do in the process of modulation? For Communication in the following devices which radio frequency bands do we use?
(i) SONAR
Answer– Sonar is a remote sensing and navigation system using sound waves. It’s primarily used underwater to detect objects and measure distances. It’s also utilized in space and aviation.
(ii) Radar
Answer– Radar, short for “Radio Detection and Ranging,” is a technology that uses radio waves to detect, locate, and identify objects such as aircraft, ships, and weather patterns. It operates by emitting radio waves, which bounce off objects and return as echoes, allowing for tracking and navigation, particularly in aviation and meteorology.
(iii) F.M. Radio
Answer– FM (Frequency Modulation) radio is a broadcast technology that uses varying radio wave frequencies to transmit audio signals. It offers highquality sound and is known for its clarity. FM radio stations are widely popular for music, news, and talk shows, providing diverse content to a broad audience.
(iv) Satellite Communication
Answer– Satellite communication involves transmitting data, voice, and video signals via artificial satellites in Earth’s orbit. It enables global communication, from television broadcasts to internet connectivity. Satellites serve various purposes, including weather forecasting, navigation, and military applications. They play a crucial role in connecting people and enabling information exchange worldwide.
5. Answer any one of the following questions in 100150 words.
a) You are provided with two identical looking spheres A and B having equal masses and radii made of different materials. Actually one of them is a solid sphere and the other is a spherical shell. Suggest an experiment to find out which of the two is hallow from within. Give reason in support of your answer.
Answer– To determine whether sphere A is a solid sphere and sphere B is a hollow spherical shell (or vice versa), you can conduct a simple experiment using the principle of rotational inertia. Here’s how you can do it:
Materials Needed:

 Sphere A (the one you suspect is a solid sphere).

 Sphere B (the one you suspect is a hollow spherical shell).

 A thin rod or a stick.

 A string.

 Stopwatch or timer.
Experiment Procedure:

 Hang sphere A and sphere B separately from a fixed point using the string so that they can rotate freely.

 Use the thin rod or stick to gently push sphere A into a rotational motion (i.e., make it swing like a pendulum). You can do this by applying a small force to set it into motion.

 Measure the time it takes for sphere A to complete one full rotation (from one side to the other side and back). Record this time as “t_solid.”

 Repeat the same process for sphere B, which is also hung on the string. Gently push sphere B into a rotational motion and measure the time it takes for it to complete one full rotation. Record this time as “t_hollow.”
Analysis:
Now, compare the times taken for the two spheres (t_solid and t_hollow). According to the law of rotational inertia:

 A solid sphere has more rotational inertia than a hollow spherical shell of the same mass and radius.

 A sphere with more rotational inertia takes more time to complete one full rotation.
If t_solid is significantly larger than t_hollow, it suggests that sphere A (the first one you tested) is the solid sphere, as it took longer to rotate, indicating it has more rotational inertia. Sphere B, in this case, would be the hollow spherical shell. The difference in rotation times is due to the difference in mass distribution between the two shapes.
Conversely, if t_hollow is significantly larger than t_solid, it suggests that sphere B (the second one you tested) is the solid sphere, as it took longer to rotate. In this case, sphere A would be the hollow spherical shell.
This experiment relies on the principle of rotational inertia, which can help differentiate between solid and hollow spherical objects based on their rotation behavior.
b) Can the affective utilization of solar energy solve our energy problem? Giving numerical calculations answer this question. In your calculations you can use the data given below:
Solar constant for earth = 1.36×10^{3} w m^{2} 2
Radius of birth = 6.4×108m
Stefan Boltzmann Constant = 5.7×10^{8 }w m1 k^{4}
Temperatures of the Surface of Sun = 6000 k
Radius of sun = 7×10^{5 }km
Radius of the orbit of earth = 1.5 x10^{2} km
Population of earth = 10 billion
Answer– To assess the potential
of solar energy, we can calculate the total power radiated by the Sun, the
power intercepted by Earth, and the energy needs of the Earth’s population.
provides insights into the feasibility of solar energy. This calculation, while illustrative, assumes complete efficiency and doesn’t account for factors like storage, transmission, or variations in sunlight. Realworld implementation would involve more nuanced considerations.
6. Prepare any one project as given below
a) Take a rubber string fix its one end to a rigid support and attach a light scale pan on its lower end. Attach a pointer just above the pan which may move freely against a vertical scale. Add weight on the pan in steps of 10g and note the position of the pointers in each case. Take 56 readings .Note the position of the pointers again while removing weights from the pan. Tabulate the data and draw case of load increasing as well as load decreasing on the same graph. Repeat the experiment using a spring in place of rubber string. Compare the graph obtained in the two cases.
Answer– The experiment you’re describing involves the study of the deformation of a rubber string and a spring under varying loads. The aim is to compare the behavior of the two materials by recording the position of a pointer against a vertical scale as the load increases and decreases. Here’s how you can proceed:
Materials Needed:

 Rubber string

 Spring

 Rigid support (e.g., a wall or a stand)

 Scale pan

 Pointer

 Weights (in steps of 10g)

 Vertical scale

 Notebook and pen to record data
Procedure:

 Fix one end of the rubber string to a rigid support, ensuring it is secure.

 Attach a light scale pan to the lower end of the rubber string. The rubber string should be in a vertical position.

 Attach a pointer just above the pan, ensuring it can move freely against a vertical scale. The pointer should be set to an initial position.

 Start adding weights to the scale pan in increments of 10g. After adding each weight, allow the system to come to equilibrium, and record the position of the pointer against the vertical scale. Do this for 56 readings, increasing the load each time.

 After obtaining the readings with increasing loads, start removing weights from the pan in the same increments, recording the position of the pointer after each weight is removed.

 Tabulate the data, with one column for increasing loads and another for decreasing loads. Include the position of the pointer in each case.

 Repeat the entire experiment using a spring instead of the rubber string. Follow the same procedure for the spring, recording the position of the pointer as you add and remove weights.
Data Analysis:

 Create two graphs on the same graph paper: a. Load (in grams) on the xaxis and the corresponding position of the pointer for the rubber string on the yaxis. b. Load (in grams) on the xaxis and the corresponding position of the pointer for the spring on the yaxis.

 Compare the two graphs. Look for differences in the behavior of the rubber string and the spring as the load increases and decreases. Observe how the materials deform and recover when subjected to a load.

 Note any differences in elasticity, stiffness, and hysteresis between the rubber string and the spring.

 Summarize your findings and draw conclusions about the differences in behavior between the two materials when subjected to varying loads.
This experiment should provide insights into the mechanical properties of rubber and springs and how they respond to applied forces. It will help you understand the differences in their deformation and recovery characteristics.
b) Kinetic Theory of gases provides us the equation p=1/3 m nc2 using this equation derives the following laws:
1. Boyle’s Law
Answer– Boyle’s Law, based on the gaseous thermal principles, states that if the pressure of a fixed amount of gas is increased while keeping the temperature constant, the product of pressure and volume remains constant. In other words, the pressure and volume of a gas are inversely proportional when the temperature is held constant.
2. Chari’s Law
Answer“Charles’s Law” is derived from the ideal gas law using the principles of thermodynamics. It states that at constant pressure (P), the volume (V) of a gas is directly proportional to its absolute temperature (T) when the quantity of gas (n) is held constant. Mathematically, it can be expressed as V/T = constant.
3. GayLussac’s Law
Answer– “GLysek’s Law” is derived based on the thermal equation of gases, where the gas pressure (p), gas mass (m), the number of electrons (n), and the charge of electrons (e) are related. According to this relationship, p = (1/3) * m * n * e².
4. Avogadro’s Law
Answer– The ideal gas law provides the equation p = (1/3) * n * e^2, where ‘p’ represents pressure, ‘n’ is the number of gas molecules, and ‘e’ is their kinetic energy. This law, known as “Avogadro’s Law,” states that the pressure of a gas is directly proportional to the kinetic energy of its molecules and is independent of their previous interactions. As a result, gases exhibit autonomous transitions between solid, liquid, and gaseous states under varying thermal conditions.
5. Daltons Law of partial pressures
Answer– Dalton’s Partial Pressure Law states that in a mixture of gases, the partial pressure of each gas is directly proportional to its mole fraction and the total pressure of the mixture. This relationship is described by the equation p = (1/3) * n * e^2, where ‘p’ is the partial pressure, ‘n’ is the mole fraction, and ‘e’ is the total pressure.
6. Graham’s Law of diffusion
Answer– The Gas Law of Graham’s Diffusion states that as the temperature of a gas increases while pressure remains constant, its speed and kinetic energy increase. This relationship arises from the ideal gas equation, where p represents pressure, m is the gas’s mass, n is the number of moles, and e is the effusion.