AP Inter 1st Year Physics Model Paper Set 1 with Solutions

Thoroughly analyzing AP Inter 1st Year Physics Model Papers Set 1 helps students identify their strengths and weaknesses.

AP Inter 1st Year Physics Model Paper Set 1 with Solutions

Time: 3 Hours
Maximum Marks: 60

Section – A

I. Answer all the following questions. Each question carries one mark. (9 × 1 = 9 Marks)

Question 1.
Which of the following statement is true ?
(1) Both light and sound waves in air are longitudinal
(2) The sound waves in air are longitudinal while the light waves are transverse
(3) Both light and sound waves in air are transverse
(4) Both light and sound waves can travel in vacuum
Answer:
(2) The sound waves in air are longitudinal while the light waves are transverse

Question 2.
Surface tension arises due to…………..
(1) Gravitational force
(2) Pressure differences
(3) Viscosity
(4) Cohesive forces
Answer:
(4) Cohesive forces

Question 3.
Which of the following is not a vector quantity?
(1) Weight
(2) Torque
(3) Momentum
(4) Potential energy
Answer:
(4) Potential energy

Question 4.
Define centripetal force.
Answer:
Centripetal force is the force acting on a body moving in a curved path that is directed towards the centre of rotation.

Question 5.
What is the value of universal gravitational constant (G) ?
Answer:
The value of the universal gravitational constant G is 6.674 x 10¹¹ Nm² / kg²

Question 6.
What is equation for elastic potential energy stored in a stretched wire ?
Answer:
∴ U= \(\frac{1}{2} \mathrm{xy} \times\left(\frac{l}{\mathrm{~L}}\right)^2 \times \mathrm{AL}]\)

Question 7.
The area under acceleration-time graph gives …………
Answer:
Change in velocity

Question 8.
The number of translational degrees of freedom for a diatomic gas is …………
Answer:
3

Question 9.
The dimensional formula of angular impulse is …………
Answer:
[ML^-2 T^-1]

Section – B

II. Answer all the following questions. Each question carries two marks. (14 × 2 = 28 Marks)

Question 10.
Define plane angle.
Answer:
Plane angle is defined as the ratio of the length of arc to the radius of the circle.

Question 11.
Displacement travelled by a body is given by S=2 t+5 t² m. What is the acceleration of that body?
Answer:
S=2 t+5 t²
⇒ v= \(\frac{\mathrm{dS}}{\mathrm{dt}}\)=2+10t
⇒ a= \(\frac{dv}{dt}\)=10 m/s²
So, acceleration =10 m/s²

Question 12.
State triangle law of vector addition.
Answer:
Triangle Law : If two vectors are represented as two sides of a triangle taken in order, their sum is given by the third side taken in reverse order.

Question 13.
What is inertia? What gives the measure of inertia?
Answer:
Inertia is the property of an object to resist changes in its state of motion or rest. Mass of the object gives the measure of its inertia.

Question 14.
State the conditions under which a force does not work.
Answer:
A force does no work under the following conditions.
Workdone,
W = \(\bar{F} \cdot \bar{d}\)
W = Fd cosθ
(i) If the displacement (s) of the body is zero, then W=0
(ii) If the angle (θ) between the force and displacement is 90°, then W=0

Question 15.
We cannot open or close the door by applying force at the hinges. Why ?
Answer:
Opening or closing the door by applying the force at the hinges is a turning effect or torque.
We know \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\).
At the hinges \(\overrightarrow{\mathrm{r}}=\overrightarrow{0}\) so, \(\overrightarrow{\mathrm{J}}=\overrightarrow{0}\). Hence no turning effect.

Question 16.
Hydrogen is in abundance around the sun but not around the earth. Explain.
Answer:
Why No Hydrogen Around Earth:
Hydrogen is very light and escapes Earth’s gravity due to high velocity.
The Sun’s strong gravity retains hydrogen in its atmosphere.

Question 17.
State modulus of elasticity.
Answer:
Modulus of Elasticity : With in the elastic limit, the ratio of stress to strain in a body is called modulus of elasticity.
Modulus of Elasticity, E= \(\frac{\text { stress }}{\text { strain }}\)

Question 18.
What is the angle of contact ?
Answer:
The angle between the tangent to the liquid surface and the solid surface, at the point of contact, inside the liquid is known as angle of contact.

Question 19.
Define emissivity.
Answer:
The ratio of the emissive power of a body to that of a black body at the same temperature is called emissivity.
e= \(\frac{E_\lambda}{e_\lambda}\)
Where, e_λ is emissive power of the black body.

Question 20.
Define thermal equilibrium. How does it lead to Zeroth law of thermodynamics?
Answer:
Thermal Equilibrium : Two systems are said to be in thermal equilibrium, if the temperatures of two systems are equal and there is no net flow of heat between them, when they are in thermal contact.

Zeroth law of thermodynamics : If two systems A and B are separately in thermal equilibrium with a third system C then the systems A and B are in thermal equilibrium with each other.

Question 21.
What is the expression between pressure and kinetic energy of a gas molecule?
Answer:
The relation between pressure ‘ P ‘ and kinetic energy of a gas is given by
\(\mathrm{P}=\frac{2}{3} \frac{\mathrm{~N} \overline{\mathrm{~K}}}{\mathrm{~V}}\)
Where \(\overline{\mathrm{K}}\) is the average kinetic energy of translation per gas molecules,
N is number of molecules and
V is volume of the gas.

Question 22.
Can a simple pendulum be used in an artificial satellite? Why?
Answer:
No.
In an artificial satellite

So, pendulum doesn’t oscillate.

Question 23.
What are beats?
Answer:
When two sound waves of slightly different frequencies travelling in the same direction interfere, waxing and wanning of sounds are heard at regular intervals of time these are called beats.

Section – C

III. Answer ANY EIGHT of the following questions. Each question carries four marks. (8 × 4 = 32 Marks)

Question 24.
Explain the terms average velocity and instantaneous velocity. When are they equal?
Answer:
Average velocity is the total displacement divided by total time :
\(v_{\text {avg }}=\frac{s}{t}\)
Instantaneous velocity is the velocity at a particular instant, found using calculus:
\(\mathrm{v}=\frac{\mathrm{dS}}{\mathrm{dt}}\)
They are equal only when velocity is constant, i.e., when there is no acceleration.

Question 25.
Define unit vector, null vector and position vector.
Answer:
1. Unit Vector : A unit vector is a vector of unit magnitude that points in a particular direction. It has :

• No dimension and only specifies direction.
• Commonly used to indicate directions along the axes in coordinate systems.

For a unit vector \(\hat{A}\) in the direction of vector \(\vec{A}\), it is given by :
\(\hat{\mathrm{A}}=\overrightarrow{\mathrm{A}}|\overrightarrow{\mathrm{~A}}|\)
Unit vectors along the \(\overrightarrow{\mathrm{x}}, \overrightarrow{\mathrm{y}}\), and \(\overrightarrow{\mathrm{z}}\) – axes are denoted as \(\hat{\mathrm{i}}, \hat{\mathrm{j}}, \hat{\mathrm{k}}\) respectively.

2. Null Vector (or Zero Vector): A null vector is a vector that has zero magnitude and no specific direction.
It is represented as :
\(\overrightarrow{0}=0 \hat{\mathrm{i}}+0 \hat{\mathrm{j}}+0 \hat{\mathrm{k}}\)
In geometrical representation, it is a point at the origin and does not change position or direction.

3. Position Vector: The position vector of a particle P located in a plane with reference to the origin 0 is :
\(\overrightarrow{\mathrm{r}}=\mathrm{x} \hat{\mathrm{i}}+\mathrm{y} \hat{\mathrm{j}}\)
where: x and y are the coordinates of point P, \(\hat{\mathrm{i}}\) and \(\hat{\mathrm{j}}\) are unit vectors along the x – and y – axes respectively.
This vector shows the position of the particle in space relative to the origin.

Question 26.
Mention the methods used to decrease friction.
Answer:

• Lubrication : Applying oil or grease reduces contact between surfaces.
• Polishing surfaces : Makes them smoother, reducing resistance.
• Using ball bearings or rollers : Converts sliding friction into rolling friction (which is much lower).
• Streamlining: In vehicles and aircraft to reduce air resistance.
• Using proper materials : Like Teflon, which has a low coefficient of friction.

Question 27.
Write the equations of motion for a particle rotating about a fixed axis.
Answer:
For angular motion with constant angular acceleration α:

These are analogous to the linear equations of motion.

Question 28.
Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particles are 100g, 150g and 200 g are taken at origin, on X -axis and in XY plane respectively. Each side of the equilateral triangle is 0.5 m long.
Answer:
Given
length of side =0.5m
Masses m₁=100g, m₂=150 g, and m₃ =200g

Question 29.
What is orbital velocity? Obtain an expression for it.
Answer:
Orbital velocity:
The minimum velocity required for a body in order to revolve around a planet in circular orbit is known as orbital velocity.

Expression :
Consider the earth of mass M and radius R.
Here the necessary centripetal force acting on the satellite is provided by the gravitational force of attraction by the earth of the satellite.

It depends on earth’s mass and the radius of orbit from Earth’s centre.

Question 30.
Define strain and explain the types of strain.
Answer:
Strain : The rate of change in dimension to the original dimension of a body is called strain.
\(\text { strain }=\frac{\text { change in dimension }}{\text { original dimension }}\)

Types of strain : There are three types they are:

• Longitudinal strain: The ratio of change in length due longitudinal force to original length of the body is called longitudinal strain.
• Volume strain: The ratio of change in volume due to normal force to original volume of the body is called volume strain.
• Shearing Strain : The ratio of relative displacement between two layers due to tangential force to the perpendicular distance between the layers of a body is called shearing strian.

Question 31.
Explain the surface tension and surface energy.
Answer:
Surface Tension : The tangential force per unit length, acting at right angles on either side of a line imagined to be drawn on the free liquid surface in equilibrium is called surface tension.
Surface Energy: The additional potential energy due to the molecular forces per unit surface area is called surface energy.
Surface Energy \(=\frac{\text { Potential energy due to molecular forces }}{\text { Surface area }}\)

Question 32.
Explain conduction, convection and radiation with examples.
Answer:
Conduction :
The process of transfer of heat energy through a medium. With out any actual movement of the particles (molecules or atoms) of the medium is called conduction. Ex: In all solids and in mercury heat flows by the method of conduction.

Convection :
The process of transfer of heat energy through a medium with actual movement of the particles (molecules or atoms) of the medium is called convection. Ex : In all fluids heat flows by the method of convection see breezes and trade winds are the examples.

Radiation :
The process of transfer of heat from one place to another even without the presence of any medium is called radiation.
Ex: Earth receives heat from the sun.

Question 33.
Explain triple point of water with the help of pressure-temperature graph.
Answer:
Triple Point:
The standard pressure and temperature at which all three states of matter (solid, liquid and vapour) coexist is known as triple point of water. For water, triple point are (P,T)=(4.58 mm of Hg, 273.16 K) or ( 0.006 atm, 0.01°C).

To study the change of states of water a graph is drawn between pressure and temperature are shown is phasor diagram. There are three curves in the phase diagram.

1. Ice line (PB) :
At all the points on this curve ice and water are in equilibrium. It has negative slope. It means as pressure increases, melting point of ice decreases.

2. Steam line (PA) :
At all the points on this curve water and steam are in equilibrium. It has positive slope. It means as pressure increases, boiling point of water also increases.

3. Sublimation line (PC) :
At all the points on this curve ice and steam are in equilibrium. It has positive slope. It means as pressure increases, sublimation point of water also increases.
The intersection of these three curves is triple point.

Question 34.
If a gas has f degrees of freedom, find the ratio of C_p and C_v
Answer:
Consider one mole of a gas, let each gas, molecule possesses ‘ f’ degress of freedom. As one mole of the gas contains N molecules, the total degrees of freedom of the system of the gas = Nf
If ‘ T ‘ is the temperature of the system, then according to the law of equipartition of energy.

Question 35.
Explain the modes of vibrations of an air column in a closed pipe.
Answer:
1st harmonic (or) Fundamental Frequency: If the air column is vibrated as shown in the fig. one-anti-node and one node are formed. The distance between successive node and anti-node is \(\frac{‘ \lambda^{\prime}}{4}\)

Here v₁ is called 1st harmonic (or) Fundamental Frequency.

3rd Harmonic (or) 1st overtone : If the air column is vibrated with one and half loop then two anti-nodes and two nodes are formed. The distance between successive node and anti-node is \(\frac{‘ \lambda^{\prime}}{4}\) and successive node is \(\frac{{ }^{\prime} \lambda}{2}\)

Here v₃ is called 3rd harmonic (or) first overtone.
5th  harmonic and 2nd overtone : If the air column is vibrated with two and half loops, then three nodes and three anti-nodes are formed.
The distance between successive node and anti-node is \(\frac{{ }^{\prime} \lambda}{4}\) and successive node is \(\frac{{ }^{\prime} \lambda^{\prime}}{2}\).

Section – D

IV. Answer ANY TWO of the following questions. Each question carries eight marks. (2 × 8 = 16 Marks)

Question 36.
Define elastic and inelastic collisions. Derive expressions for the final velocities of bodies in one dimensional elastic collision, when one body collides with other body which is initially at rest.
Answer:
A strong interaction between bodies which involves exchange of momenta is called collision. They are two types.

• Elastic collision
• Inelastic collision

Elastic collision : The collisions in which both momentum and kinetic energy are conserved are known as elastic collisions.

Inelastic collisions : The collisions in which kinetic energy is not conserved but momentum is conserved are known as inelastic collisions. Here the loss of kinetic energy appears in the form of heat or other forms of energy.

One – Dimensional Elastic Collision: If the velocities of the objects involved in collision are along the same straight line before and after collisions then such collisions are known as one dimensional collisions.

Consider two smooth spheres moving along a straight line joining their centres. Let nij and m₂ are the masses of the two bodies. Suppose they undergo one dimensional elastic collision. Before collision, Let u₁ and u₂ are their velocities. After collision, let v₁ and v₂ are their final velocities. Assume that u₁ > u₂
From the law of conservation of linear momentum.
Momentum of the system before collision = momentum of the system after collision.
m₁u₁ + m₂u₂= m₁v₁ + m₂v₂
⇒ m, (u,-v,) – m₂ (v₂-u₂) ————— (1)
In case of elastic collision, kinetic energy is also conserved.
Hence,
kinetic energy of the system before collision = kinetic energy of the system after collision.

Hence,
relative velocity of approach = relative velocity of separation. Before collison = After collision
From equation (D we get v₂ = u_r – u₂ + v_t ……….(4)

From equations (5) & (6), It is concluded that the final velocities of both the bodies depend on their initial velocities and masses.

Question 37.
Define two specific heat capacities of a gas and derive the relation between them on the basis of first law of thermodynamics.
Answer:
Definition: The two specific heat capacities of a gas, C_p (specific heat at constant pressure) and C_v (specific heat at constant volume), represent the amount of heat required to raise the temperature of a unit mass of the gas by one degree at constant pressure and volume respectively.
Derivation:

Consider one mole of an ideal gas contained in a cylinder provided with a frictionless piston.
(i) Let ‘A’ be the area of piston and P, V and T be the pressure, volume and temperature of the gas respectively.
(ii) When the gas is heated at constant volume so that it’s temperature increas­es by ‘dT’ the heat supplied dQ is utilized to increase the internal energy of the gas only.
dQ = dU = 1 x C_v x dT
∴ dQ = C_vdT ……………….. (1)

iv) When the gas is heated at constant pressure it’s temperature increase through dT the heat supplied is dQ’ is utilized to increase the internal en­ergy do and to dU external work dW by displacing the piston through a dis­tance dx.
dQ’ = 1 x C_p x dT
∴ dQ’ = C_pdT …………. (2)
From the fist law of thermodynamics, dQ’ = dU + dW
C_pdT = (V dT + dW ……………..(3)
Let F is the force acting on the piston and dX is the distance moved. Then workdone dW = F. dx
Let P is the atmospheric pressure outside the piston. Then force on the piston is given by
F = PA
dW = PAdx
From (3) we have C_pdT = C_vdT + PdV
⇒ CpdT – C_vdT = PdV     ⇒ (C_p– C_v)dT = PdV ………….(4)
From ideal gas equation PV = RT
PdV = RdT ………. (5)
Substituting (5) in (U) we get
⇒ (C_p-C_v)dT = R.dT
∴ C_p-C_V = R.

(a) Consider a simple pendulum of length T consists a bob of mass ‘m’ is suspend­ed from a rigid support ‘s’.
The pendulum pulled through a side with small angular displacement ‘θ’ with released then it begins to oscillation about the mean position ‘O’ at any instant of time, the pendulum at point A, the weight ‘mg’ resolved into two components.
‘mg cos0’ balanced by the tension in a string, ‘mg sin θ’ pulled the pendulum to its means position, hence ‘mg sin θ’ is called restoring force F = – mg sin θ

If ‘0’ is very small, then sinθ ≈ θ
F = – mg θ
From Newton’s II^nd law we have
F = ma

∴ The time period is independent of the amplitude of oscillation as long as the amplitude is so small such that the bob oscillates along a straight line.

Second’s Pendulum:
The pendulum whose time period is two seconds is called seconds pendulum.

Question 38.
(a) Show that the motion of a simple pendulum is simple harmonic and hence derive the Equation for its time period. What is second’s pendulum?
(b) On an average a human heart is found to beat 75 times in a minute. Calculate its frequency and time period.
Answer:
b) The beat frequency of heart
=75 / 1 min
= \(\frac{75}{60 \mathrm{~s}}\)
=1.25/ s
∴ Frequency =1.25 Hz
The time period T = 1/1.25
= 0.8s
∴ Time period T =0.8 s