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Questions
1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1

Consider a simple pendulum undergoing simple harmonic motion with a time period $T$, and a fixed amplitude $\theta_0$ of angular oscillation. Its angular momentum about the point of suspension exhibits an oscillatory behaviour with an amplitude $A$. Which of the following relations between $A$ and $T$ is correct?

A
$A \propto T^1$
B
$A \propto T^2$
C
$A \propto T^3$
D
$A \propto T^4$
2
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Consider the motion of a particle along the $x$-axis. The position of the particle varies with time as $x(t)=\sin ^2(\omega t) \cos ^3(\omega t)$, where $\omega$ is a constant. What is the time period of the motion?
A
$\frac{2 \pi}{\omega}$
B
$\frac{2 \pi}{3 \omega}$
C
$\frac{2 \pi}{5 \omega}$
D
$\frac{2 \pi}{15 \omega}$
3
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Consider a solid sphere of radius $R$ floating in a pond with half of the sphere submerged. The sphere is pushed vertically downwards at the topmost point and released, such that it executes a simple harmonic motion. Acceleration due to gravity is $g$. What is the time period of oscillation?
A
$2 \pi \sqrt{\frac{2 R}{g}}$
B
$2 \pi \sqrt{\frac{R}{g}}$
C
$2 \pi \sqrt{\frac{3 R}{2 g}}$
D
$2 \pi \sqrt{\frac{2 R}{3 g}}$
IAT (IISER) Subjects
Physics
Mechanics
Units & Measurement and Dimensions Laws of Motion Circular Motion Work, Energy and Power Rotational Motion Gravitation Simple Harmonic Motion Fluid Mechanics Heat and Thermodynamics
Optics
Ray Optics
Electromagnetism
Electrostatics Current Electricity Capacitor Moving Charges and Magnetism Electromagnetic Induction Alternating Current Electromagnetic Waves
Modern Physics
Atoms and Nuclei Dual Nature of Radiation Semiconductor Devices and Logic Gates
Chemistry
Physical Chemistry
Atomic Structure Thermodynamics Ionic Equilibrium Liquid Solution Solid State Electrochemistry Chemical Kinetics
Inorganic Chemistry
Periodic Table and Periodicity Chemical Bonding and Molecular Structure p-Block Elements Coordination Compounds
Organic Chemistry
General Organic Chemistry Isomerism Hydrocarbons Haloalkanes and Haloarenes Alcohol, Phenols and Ethers Carboxylic Acids and Its Derivatives Compounds Containing Nitrogen Biomolecules
Mathematics
Algebra
Sequences and Series Probability Sets and Relations Binomial Theorem Three Dimensional Geometry Matrices and Determinants Complex Numbers
Trigonometry
Trigonometric Equations Properties of Triangles
Calculus
Functions Limits, Continuity and Differentiability Application of Derivatives Definite Integration Differential Equations
Coordinate Geometry
Straight Lines and Pair of Straight Lines Circle
Biology
Botany
Cell - The Unit of Life Cell Cycle and Cell Division Sexual Reproduction in Flowering Plants Microbes in Human Welfare Anatomy of Flowering Plants Mineral Nutrition Biotechnology: Principles and Processes Morphology of Flowering Plants Photosynthesis in Higher Plants Principles of Inheritance and Variation Molecular Basis of Inheritance Organisms and Populations Ecosystem
Zoology
Human Health and Diseases Locomotion and Movement Reproduction in Organisms Digestion and Absorption Excretory Products and Their Elimination Animal Kingdom Breathing and Exchange of Gases
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