A bullet of mass \(10^{-2}\) kg and velocity \(200\) m/s gets embedded inside the bob of mass \(1\) kg of a simple pendulum. The maximum height that the system rises by is_____ cm.
A bullet of mass \(10^{-2}\) kg and velocity \(200\) m/s gets embedded inside the bob of mass \(1\) kg of a simple pendulum. The maximum height that the system rises by is_____ cm.
Solution and Explanation
The Correct Answer is : 20
Momentum conservation :
\(10^{-2} \times 200 ≃ 1 × v …(1)\)
Energy conservation :
v\(=\sqrt{2gh}\ \ \ ....(2)\)
\(⇒h=\frac{v^2}{2g}\)
\(=\frac{4}{20}m=20cm\)
Top Questions on Energy in simple harmonic motion
- A ring and a solid sphere are released from rest from the same height on enough rough inclined surface. The ratio of their speed when they reach the bottom is \( \sqrt{\frac{7}{x}} \) m/s, then \( x \) is ______.
- JEE Main - 2025
- Physics
- Energy in simple harmonic motion
- A pendulum of length 4 m is located at a height R above the earth's surface.The period of the simple pendulum is \(2\pi\sqrt{\frac{8}{x}}\) seconds. Find x.
- JEE Main - 2024
- Physics
- Energy in simple harmonic motion
- Find the ratio of K.E. and P.E. when a particle performs SHM when it is at \( \frac{1}{n} \) times of its amplitude from the mean position.
- MHT CET - 2024
- Physics
- Energy in simple harmonic motion
From a height of 'h' above the ground, a ball is projected up at an angle \( 30^\circ \) with the horizontal. If the ball strikes the ground with a speed of 1.25 times its initial speed of \( 40 \ ms^{-1} \), the value of 'h' is:
- TS EAMCET - 2024
- Physics
- Energy in simple harmonic motion
- Impending motion is opposed by:
- KEAM - 2024
- Physics
- Energy in simple harmonic motion
Questions Asked in JEE Main exam
- Match List - I with List - II. List - I (Partial Derivatives) \(and\) List - II (Thermodynamic Quantity)
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Thermodynamics
- Let $ \vec{a} $ and $ \vec{b} $ be the vectors of the same magnitude such that $ \frac{| \vec{a} + \vec{b} | + | \vec{a} - \vec{b} |}{| \vec{a} + \vec{b} | - | \vec{a} - \vec{b} |} = \sqrt{2} + 1. \quad \text{Then } \frac{| \vec{a} + \vec{b} |^2}{| \vec{a} |^2} \text{ is:} $
- JEE Main - 2025
- Vector Algebra
- Let the distance between two parallel lines be 5 units and a point \( P \) lies between the lines at a unit distance from one of them. An equilateral triangle \( POR \) is formed such that \( Q \) lies on one of the parallel lines, while \( R \) lies on the other. Then \( (QR)^2 \) is equal to _____________.
- JEE Main - 2025
- Coordinate Geometry
Let \( a \in \mathbb{R} \) and \( A \) be a matrix of order \( 3 \times 3 \) such that \( \det(A) = -4 \) and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where \( I \) is the identity matrix of order \( 3 \times 3 \).
If \( \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) \) is \( 2^m 3^n \), \( m, n \in \{ 0, 1, 2, \dots, 20 \} \), then \( m + n \) is equal to:
- JEE Main - 2025
- Determinants
- Let $ A = \left\{ \theta \in [0, 2\pi] : \Re\left( \frac{2 \cos \theta + i \sin \theta}{\cos \theta - 3i \sin \theta} \right) = 0 \right\} $. Then $ \sum_{\theta \in A} \theta^2 $ is equal to:
- JEE Main - 2025
- Trigonometric Equations
Concepts Used:
Energy In Simple Harmonic Motion
We can note there involves a continuous interchange of potential and kinetic energy in a simple harmonic motion. The system that performs simple harmonic motion is called the harmonic oscillator.
Case 1: When the potential energy is zero, and the kinetic energy is a maximum at the equilibrium point where maximum displacement takes place.
Case 2: When the potential energy is maximum, and the kinetic energy is zero, at a maximum displacement point from the equilibrium point.
Case 3: The motion of the oscillating body has different values of potential and kinetic energy at other points.