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Karnataka 1st PUC Mid Term Question Papers 

1st PUC Physics Midterm Numericals: Numerical questions are an important part of the 1st PUC Physics midterm exam. These questions test how well students can understand a problem and use the correct Physics formula to find the answer.

The main numerical questions are usually based on topics such as work, energy, power, laws of motion, rotational motion, kinematics, projectile motion, and gravitation. Students should learn the basic formulas and practise different types of questions. Regular practice can help improve calculation speed and reduce mistakes during the exam.

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Work, Energy, and Power Numericals

It includes questions based on work, force, displacement, energy, and power. Students should first identify the values given in the question and then select the correct formula.

1. Work Done

Work done questions can be asked in different forms.
When force and displacement are in the same direction:
Work = Force × Displacement
For example, if a force of 8 N moves an object through 9 m:
Work = 8 × 9
Work = 72 J
When force and displacement are given as vectors, use the dot product:
Work = (Fx × sx) + (Fy × sy) + (Fz × sz)
Here, Fx, Fy, and Fz are the force components. sx, sy, and sz are the displacement components.
When force acts at an angle with displacement:
Work = Force × Displacement × cos θ
Here, θ is the angle between force and displacement.

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2. Kinetic Energy

Kinetic energy is the energy possessed by a moving object. It depends on the mass and velocity of the object.
Kinetic Energy = 1/2 × Mass × Velocity²
Students should carefully check the units of mass and velocity before solving the question.

System of Particles and Rotational Motion Numericals

This chapter deals with the motion of objects around an axis. Some important relations between linear and rotational motion are:
Force (F) → Torque (T)
Mass (m) → Moment of Inertia (I)
Velocity (v) → Angular Velocity (ω)
Momentum (p) → Angular Momentum (L)

1. Power and Torque

Numerical questions may ask for the power needed by an engine to rotate an object at a particular angular speed.
Power = Torque × Angular Velocity
If torque and angular velocity are given, multiply the two values to find power.

2. Centre of Mass

Centre of mass questions may give different masses placed at different points. The position of the centre of mass can be found using weighted averages.
For three particles:
Xcm = (m1 × x1 + m2 × x2 + m3 × x3) / (m1 + m2 + m3)
Ycm = (m1 × y1 + m2 × y2 + m3 × y3) / (m1 + m2 + m3)
Here, m represents mass, while x and y represent the coordinates of the particles.

3. Rotational Motion

Questions may ask about angular acceleration, angular velocity, revolutions, angular momentum, or rotational kinetic energy.
For a solid cylinder rotating around its central axis:
Moment of Inertia = 1/2 × M × R²
Angular momentum is calculated using:
Angular Momentum = Moment of Inertia × Angular Velocity
L = I × ω
Rotational kinetic energy is:
Rotational Kinetic Energy = 1/2 × I × Angular Velocity²
K = 1/2 × I × ω²
Students should remember the correct formula for each quantity.

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Laws of Motion Numericals

Laws of Motion numericals mainly include force, friction, equilibrium, momentum, and impulse.

1. Equilibrium of Forces

An object is in equilibrium when the total force acting on it is zero.
The conditions are:
ΣFx = 0
ΣFy = 0
These equations can be used to find unknown forces, tensions, or angles in a problem.

2. Collision and Impulse

Impulse is related to the change in momentum.
Impulse = Final Momentum - Initial Momentum
For a ball of mass m moving with velocity v and rebounding with the same speed in the opposite direction:
Impulse = m(-v) - mv
Impulse = -2mv
The magnitude of impulse is:
Magnitude of Impulse = 2mv

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3. Motion Against Resistance

Some questions give an applied force and a resistive force. The first step is to find the net force.
Net Force = Applied Force - Resistive Force
Then use Newton's second law:
Net Force = Mass × Acceleration
Fnet = m × a
After finding acceleration, the correct equation of motion can be used to calculate distance or velocity.

Kinematics and Projectile Motion Numericals

1. Retardation

Retardation means a reduction in the velocity of an object. Questions may provide the initial velocity and stopping distance.
The equation used is:
v² = u² - 2as
If the final velocity is zero:
a = u² / 2s
Here:
u = Initial velocity
v = Final velocity
a = Acceleration or retardation
s = Distance
Students should use the correct signs while solving these questions.

2. Projectile Motion

Projectile motion questions may ask for the angle that gives the maximum horizontal range.
For a projectile moving on level ground:
Angle of Projection = 45°
The maximum range is:
Rmax = u² / g
Here, u is the initial velocity and g is the acceleration due to gravity.

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Gravitation Numericals

Planetary Escape Velocity

Escape velocity is the minimum speed needed for an object to escape the gravitational pull of a planet.
The formula is:
ve = √(2GM / R)
Here:
G = Gravitational constant
M = Mass of the planet
R = Radius of the planet
The escape velocity of Earth is about 11.2 km/s.
When comparing another planet with Earth, the formula is:
vplanet / vearth = √[(Mplanet / Mearth) × (Rearth / Rplanet)]
This formula helps find the escape velocity when the mass and radius of another planet are given in comparison with Earth.

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