Question
When you push your bicycle up on an incline the potential energy of the bicyle and yourself increases. Where does this energy come from?
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Answer
When a person pushes his bicycle up on an inclined plane, the potential energies of the bicycle and the person increase because moving up on the inclined plane the kinetic energy decreases. and as mechanical energy is sum of kinetic energy and potential energy, and remains constant for a conservative system. Therefore, potential energy must increase in this case.
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Read the passage given below and answer the following questions from $i$ to $v.$ we consider the motion of a projectile. An object that is in flight after being thrown or projected is called a projectile. Such a projectile might be a football, a cricket ball, a baseball or any other object. The motion of a projectile may be thought of as the result of two separate, simultaneously occurring components of motions. One component is along a horizontal direction without any acceleration and the other along the vertical direction with constant acceleration due to the force of gravity. It was Galileo who first stated this independency of the horizontal and the vertical components of projectile motion in his Dialogue on the great world systems. Horizontal range of a projectile: The horizontal distance travelled by a projectile from its initial position $(x = y = 0)$ to the position where it passes $y = 0$ during its fall is called the horizontal range, $R$. It is the distance travelled during the time of flight $T_f .$ Therefore, the range $\text{R is R} =(\text{v}_o\cos\theta_o(\text{T}_\text{f})$
$\text{R}=\frac{(\text{v}_\text{o}\cos\theta_\text{o})(2\text{v}_\text{o}\sin\theta_\text{o})}{\text{g}}$
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→$\text{R}=\frac{(\text{v}_\text{o}\cos\theta_\text{o})(2\text{v}_\text{o}\sin\theta_\text{o})}{\text{g}}$
$\text{R}=\frac{(\text{v}_\text{o}^{2}\sin\theta_\text{o})}{g}$ This shows that for a given projection velocity, $R$ is maximum when $2\theta_\text{o}$ is maximum, i.e., when $\theta_\text{o}=45^\circ.$ The maximum horizontal range is, therefore $\text{R}=\frac{\text{v}_\text{o}^2}{g}$ Maximum height of a projectile: Maximum height that can be achieved during projectile and it is given by: $\text{H}_\text{m}=\frac{\text{(v}_\text{o}\sin\theta)^2}{2g}$
- Range in projectile motion is maximum when $\theta^\circ:$
- $45^0$
- $0^0$
- $90^0$
- None of these
- Who was first stated this independency of the horizontal and the vertical components of projectile motion in his Dialogue on the great world system?
- Galileo
- Newton
- Einstein
- None of these
- What is projectile motion?
- What is horizontal range of projectile? Give its formula:
- What is maximum height of projectile? Give its formula:
Read the passage given below and answer the following questions from 1 to 5. In general, the errors in measurement can be broadly classified as (a) systematic errors and (b) random errors. Systematic errors: The systematic errors are those errors that tend to be in one direction, either positive or negative. Some of the sources of systematic errors are: (a) Instrumental errors that arise from the errors due to imperfect design or calibration of the measuring instrument, zero error in the instrument, etc. For example, the temperature graduations of a thermometer may be inadequately calibrated (it may read 104 °C at the boiling point of water at STP whereas it should read 100 °C); in a vernier calipers the zero mark of vernier scale may not coincide with the zero mark of the main scale, or simply an ordinary metre scale may be worn off at one end. (b) Imperfection in experimental technique or procedure to determine the temperature of a human body, a thermometer placed under the armpit will always give a temperature lowers than the actual value of the body temperature. (c) Personal errors that arise due to an individual’s bias, lack of proper setting of the apparatus or individual’s carelessness in taking observations without observing proper precautions, etc. For example, if you, by habit, always hold your head a bit too far to the right while reading the position of a needle on the scale, you will introduce an error due to parallax.Systematic errors can be minimized by improving experimental techniques, selecting better instruments and removing personal bias as far as possible. For a given set-up, these errors may be estimated to a certain extent and the necessary corrections may be applied to the readings. Random errors:The random errors are those errors, which occur irregularly and hence are random with respect to sign and size. These can arise due to random and unpredictable fluctuations in experimental conditions (e.g. unpredictable fluctuations in temperature, voltage), personal (unbiased) errors by the observer taking readings, etc. For example, when the same person repeats the same observation, it is very likely that he may get different readings every time. Least count error: The smallest value that can be measured by the measuring instrument is called its least count. All the readings or measured values are good only up to this value. The least count error is the error associated with the resolution of the instrument.
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- Instrumental error
- Random error
- Least count error
- None of the above
- The errors which occur irregularly
- Instrumental error
- Personal error
- Random error
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- Write a note on random error
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- Work by the ground on the losing team.
- Total external work on the two teams.
Read the passage given below and answer the following questions from 1 to 5. PE of Spring There are many types of spring. Important among these are helical and spiral springs as shown in figure.
Usually, we assume that the springs are massless. Therefore, work done is stored in the spring in the form of elastic potential energy of the spring. Thus, potential energy of a spring is the energy associated with the state of compression or expansion of an elastic spring.
Usually, we assume that the springs are massless. Therefore, work done is stored in the spring in the form of elastic potential energy of the spring. Thus, potential energy of a spring is the energy associated with the state of compression or expansion of an elastic spring.
- The potential energy of a body is increases in which of the following cases?
- If work is done by conservative force
- If work is done against conservative force
- If work is done by non-conservative force
- If work is done against non- conservative force
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- x = 0
- gravitational force is constant
- infinite distance from the gravitational source
- All of the above
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- 2 : 3
- 3 : 2
- 4 : 9
- 9 : 4
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- 27 J
- 30 J
- 33 J
- 36 J
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- 10 J
- 20 J
- 30 J
- 40 J