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Questions and Answers
A projectile is launched at $10 m/s$ at an angle of $60°$ to the horizontal. At a certain time, its velocity makes an angle of $30°$. What is its speed at this instant?
A projectile is launched at $10 m/s$ at an angle of $60°$ to the horizontal. At a certain time, its velocity makes an angle of $30°$. What is its speed at this instant?
- $\frac{5}{\sqrt{3}}$
- $\frac{10}{\sqrt{3}}$
- $5\sqrt{3}$ (correct)
- $10\sqrt{3}$
Two blocks of masses 2 kg and 4 kg are connected by a light string on a smooth horizontal surface. They are pulled by forces of 13 N and 24 N as shown. What is the tension in the string connecting the two blocks?
Two blocks of masses 2 kg and 4 kg are connected by a light string on a smooth horizontal surface. They are pulled by forces of 13 N and 24 N as shown. What is the tension in the string connecting the two blocks?
- 4 N
- Zero
- 17.5 N
- 11 N (correct)
The acceleration due to gravity is $g_1$ at a height $h = R/2$ (where R is the radius of the Earth) from the surface. It is again equal to $g_1$ at a depth $d$ below the surface. What is the ratio $d/R$?
The acceleration due to gravity is $g_1$ at a height $h = R/2$ (where R is the radius of the Earth) from the surface. It is again equal to $g_1$ at a depth $d$ below the surface. What is the ratio $d/R$?
- $\frac{4}{9}$
- $\frac{1}{3}$
- $\frac{7}{9}$
- $\frac{5}{9}$ (correct)
If $Z = \frac{A^3B^{1/3}}{CD^{3/2}}$ and the percentage errors in the measurements of A, B, C, and D are 1%, 3%, 2%, and 4% respectively, what is the percentage error in the calculation of Z?
If $Z = \frac{A^3B^{1/3}}{CD^{3/2}}$ and the percentage errors in the measurements of A, B, C, and D are 1%, 3%, 2%, and 4% respectively, what is the percentage error in the calculation of Z?
A projectile is fired with an initial velocity of 10 m/s at an angle of 60 degrees with the horizontal. What is the approximate magnitude of the vertical component of the projectile's velocity at the start?
A projectile is fired with an initial velocity of 10 m/s at an angle of 60 degrees with the horizontal. What is the approximate magnitude of the vertical component of the projectile's velocity at the start?
Two blocks connected by a string are being pulled across a smooth surface. If the tension in the string is not zero, what must be true about the forces acting on the blocks?
Two blocks connected by a string are being pulled across a smooth surface. If the tension in the string is not zero, what must be true about the forces acting on the blocks?
How does the gravitational acceleration change when moving from the surface of the Earth to a height equal to half the Earth's radius ($R/2$)?
How does the gravitational acceleration change when moving from the surface of the Earth to a height equal to half the Earth's radius ($R/2$)?
In an experiment, the value of Z is calculated using measured values of A, B, C, and D. If variable C has the most significant impact on the uncertainty in Z, which of the following should be prioritized to improve the accuracy of Z?
In an experiment, the value of Z is calculated using measured values of A, B, C, and D. If variable C has the most significant impact on the uncertainty in Z, which of the following should be prioritized to improve the accuracy of Z?
Two metallic blocks, M1 and M2, of the same cross-sectional area are connected. If the length of M1 is twice that of M2, and the temperature difference across both blocks is maintained during steady state, what can be said about the amount of heat flowing through the two blocks?
Two metallic blocks, M1 and M2, of the same cross-sectional area are connected. If the length of M1 is twice that of M2, and the temperature difference across both blocks is maintained during steady state, what can be said about the amount of heat flowing through the two blocks?
A projectile is launched upwards at an angle. At the highest point of its trajectory, which of the following statements is true?
A projectile is launched upwards at an angle. At the highest point of its trajectory, which of the following statements is true?
Two blocks are connected by a string and pulled with a constant force. If the string suddenly breaks, what happens to the acceleration of the blocks?
Two blocks are connected by a string and pulled with a constant force. If the string suddenly breaks, what happens to the acceleration of the blocks?
Gravitational acceleration changes with altitude. How does it affect the calculation of potential energy of an object lifted to a height $h$ above the Earth's surface?
Gravitational acceleration changes with altitude. How does it affect the calculation of potential energy of an object lifted to a height $h$ above the Earth's surface?
When calculating a value Z from other measured parameters, how does a random error in one of the parameters affect the final result?
When calculating a value Z from other measured parameters, how does a random error in one of the parameters affect the final result?
In a steady-state heat conduction scenario involving two blocks in series, what determines the rate of heat flow through the blocks?
In a steady-state heat conduction scenario involving two blocks in series, what determines the rate of heat flow through the blocks?
A ball is thrown upwards. Considering air resistance, what is true about the time it takes to go up versus the time it takes to come down to its initial position?
A ball is thrown upwards. Considering air resistance, what is true about the time it takes to go up versus the time it takes to come down to its initial position?
Two blocks of different masses are connected by a string. A force is applied to pull them across a frictionless surface. How does the tension in the string relate to the masses of the blocks?
Two blocks of different masses are connected by a string. A force is applied to pull them across a frictionless surface. How does the tension in the string relate to the masses of the blocks?
Imagine the radius of the Earth were to double suddenly, without any change in its mass. How would your weight change?
Imagine the radius of the Earth were to double suddenly, without any change in its mass. How would your weight change?
How does systematic error differ from random error in experimental measurements?
How does systematic error differ from random error in experimental measurements?
Two materials with different thermal conductivities are used as insulators. Which factor most significantly determines the rate of heat transfer through them?
Two materials with different thermal conductivities are used as insulators. Which factor most significantly determines the rate of heat transfer through them?
Flashcards
Horizontal Velocity of a Projectile
Horizontal Velocity of a Projectile
The horizontal velocity of a projectile remains constant throughout its flight, as there is no horizontal acceleration (ignoring air resistance).
Newton's Second Law
Newton's Second Law
Relates the net force acting on an object to its mass and acceleration. F_net = ma.
Tension Force
Tension Force
The tension in a string connecting two blocks is the force transmitted through the string when it is pulled from opposite ends.
Gravity Variation with Height/Depth
Gravity Variation with Height/Depth
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Error Propagation
Error Propagation
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Thermal Conductivity
Thermal Conductivity
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Study Notes
- Data compression involves reducing the size of data for efficient storage or transmission.
Lossless Compression
- Original data can be perfectly recovered.
- Examples include Run Length Encoding (RLE), Huffman Coding, and Lempel-Ziv Algorithms.
Lossy Compression
- Some data is lost during compression, so the recovered data is not identical to the original.
- Examples include JPEG, MPEG, and MP3.
Run Length Encoding (RLE)
- Consecutive runs of the same symbol are replaced with a single symbol and a count of the run length.
- RLE is simple and efficient if data contains long runs of identical symbols.
- RLE is used in fax machines.
- Example: Input "wwwwwwwhhhtttteeeee" becomes "w6h3t4e5".
Huffman Coding
- It uses variable length encoding, assigns short codes to frequent symbols and long codes to infrequent ones.
- Example Input: ABRACADABRA
- Character Frequencies: A:5, B:2, R:2, C:1, D:1
Huffman Tree Construction
- A tree is constructed bottom-up using symbol frequencies.
- Two nodes with the smallest frequencies are picked and a new parent node is created.
- The children of the new node are the picked nodes.
- Frequency of the parent node is the sum of the frequencies of the children.
- The process repeats until a single tree is formed.
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