Question
A collision experiment is done on a horizontal table kept in an elevator. Do you expect a change in the results if the elevator is accelerated up or down because of the noninertial character of the frame?
✓
Answer
Velocity and mass are only two components that affect collision between two bodies so in this change in acceleration due to gravity will not affect the collision between two bodies. (if kept horizontally)
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In tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?
- Work by the winning team on the losing team.
- Work by the losing team on the winning team.
- Work by the ground on the winning team.
- 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.
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.
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.
- The errors due to imperfect design or calibration of the measuring instrument:
- Instrumental error
- Random error
- Least count error
- None of the above
- The errors which occur irregularly
- Instrumental error
- Personal error
- Random error
- None of these
- Write a note on least count error
- Write a note on random error
- Write a note on systematic error
Read the passage given below and answer the following questions from 1 to 5.
Power is defined as the time rate at which work is done or energy is transferred. The average power of a force is defined as the ratio of the work, W, to the total time t taken
Pav = W/t
The instantaneous power is defined as the limiting value of the average power as time interval approaches zero.
P = dw/dt
The work dW done by a force F for a displacement dr is dW = F.dr. The instantaneous power can also be expressed as
P = F.dr/dt
P = F.v
Where v is the instantaneous velocity when the force is F. Power, like work and energy, is a scalar quantity. Its dimensions are [ML2 T-3]. In the SI, its unit is called a watt (W). The watt is 1 J s-1. The unit of power is named after James Watt, one of the innovators of the steam engine in the eighteenth century. There is another unit of power, namely the horse-power (hp)
1 hp = 746W
This unit is still used to describe the output of automobiles, motorbikes.
Power is defined as the time rate at which work is done or energy is transferred. The average power of a force is defined as the ratio of the work, W, to the total time t taken
Pav = W/t
The instantaneous power is defined as the limiting value of the average power as time interval approaches zero.
P = dw/dt
The work dW done by a force F for a displacement dr is dW = F.dr. The instantaneous power can also be expressed as
P = F.dr/dt
P = F.v
Where v is the instantaneous velocity when the force is F. Power, like work and energy, is a scalar quantity. Its dimensions are [ML2 T-3]. In the SI, its unit is called a watt (W). The watt is 1 J s-1. The unit of power is named after James Watt, one of the innovators of the steam engine in the eighteenth century. There is another unit of power, namely the horse-power (hp)
1 hp = 746W
This unit is still used to describe the output of automobiles, motorbikes.
- The time rate at which work is done or energy is transferred is called as:
- Energy
- Force
- Power
- None of these
- Limiting value of power as time interval approaches zero is called as:
- Average power
- Instantaneous power
- Both a and b
- None of these
- Power is directly proportional to:
- Force
- Velocity
- Both
- None of these
- Define instantaneous power. Give its SI unit and dimensions.
- 1 horse power is equal to how many watt?
To keep valuable instruments away from the earth's magnetic field, they are enclosed in iron boxes. Explain.
The electron beam in a colour TV is accelerated through 32kV and then strikes the screen. What is the wavelength of the most energetic X-ray photon?
Read the passage given below and answer the following questions from (i) to (v).
A system is said to be isolated if no exchange or transfer of heat occurs between the system and its surroundings. When different parts of an isolated system are at different temperature a quantity of heat transfers from the part at higher temperature to the part at lower temperature. The heat lost by the part at higher temperature is equal to the heat gained by the part at lower temperature. Calorimetry means measurement of heat. When a body at higher temperature is brought in contact with another body at lower temperature, the heat lost by the hot body is equal to the heat gained by the colder body, provided no heat is allowed to escape to the surroundings. A device in which heat measurement can be done is called a calorimeter. It consists of a metallic vessel and stirrer of the same material, like copper or aluminium. The vessel is kept inside a wooden jacket, which contains heat insulating material. Matter normally exists in three states: solid, liquid and gas. A transition from one of these states to another is called a change of state. Two common changes of states are solid to liquid and liquid to gas (and, vice versa). These changes can occur when the exchange of heat takes place between the substance and its surroundings. The change of state from solid to liquid is called melting and from liquid to solid is called fusion. It is observed that the temperature remains constant until the entire amount of the solid substance melts. That is, both the solid and the liquid states of the substance coexist in thermal equilibrium during the change of states from solid to liquid. The temperature at which the solid and the liquid states of the substance is in thermal equilibrium with each other is called its melting point. The change of state from liquid to vapour (or gas) is called vaporisation. It is observed that the temperature remains constant until the entire amount of the liquid is converted into vapour. That is, both the liquid and vapour states of the substance coexist in thermal equilibrium, during the change of state from liquid to vapour. The temperature at which the liquid and the vapour states of the substance coexist is called its boiling point. The change from solid state to vapour state without passing through the liquid state is called sublimation, and the substance is said to sublime. Dry ice (solid CO2) sublimes, so also iodine. During sublimation both the solid and vapour states of a substance coexist in thermal equilibrium.
A system is said to be isolated if no exchange or transfer of heat occurs between the system and its surroundings. When different parts of an isolated system are at different temperature a quantity of heat transfers from the part at higher temperature to the part at lower temperature. The heat lost by the part at higher temperature is equal to the heat gained by the part at lower temperature. Calorimetry means measurement of heat. When a body at higher temperature is brought in contact with another body at lower temperature, the heat lost by the hot body is equal to the heat gained by the colder body, provided no heat is allowed to escape to the surroundings. A device in which heat measurement can be done is called a calorimeter. It consists of a metallic vessel and stirrer of the same material, like copper or aluminium. The vessel is kept inside a wooden jacket, which contains heat insulating material. Matter normally exists in three states: solid, liquid and gas. A transition from one of these states to another is called a change of state. Two common changes of states are solid to liquid and liquid to gas (and, vice versa). These changes can occur when the exchange of heat takes place between the substance and its surroundings. The change of state from solid to liquid is called melting and from liquid to solid is called fusion. It is observed that the temperature remains constant until the entire amount of the solid substance melts. That is, both the solid and the liquid states of the substance coexist in thermal equilibrium during the change of states from solid to liquid. The temperature at which the solid and the liquid states of the substance is in thermal equilibrium with each other is called its melting point. The change of state from liquid to vapour (or gas) is called vaporisation. It is observed that the temperature remains constant until the entire amount of the liquid is converted into vapour. That is, both the liquid and vapour states of the substance coexist in thermal equilibrium, during the change of state from liquid to vapour. The temperature at which the liquid and the vapour states of the substance coexist is called its boiling point. The change from solid state to vapour state without passing through the liquid state is called sublimation, and the substance is said to sublime. Dry ice (solid CO2) sublimes, so also iodine. During sublimation both the solid and vapour states of a substance coexist in thermal equilibrium.
- Device used for measurement of heat is:
- Calorimeter
- Thermometer
- Both a and b
- No one of these
- The change of state from solid to liquid is called:
- Melting
- Vaporization
- Sublimation
- None of these
- Define melting point and boiling point:
- What is sublimation?
- Define fusion process:
Let us assume that our galaxy consists of $2.5 \times 10^{11}$ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky way to be $10^5 ly$.
→A slide projector has to project a 35mm slide (35mm × 23mm) on a 2m × 2m screen at a distance of 10m from the lens. What should be the focal length of the lens in the projector?
$\int\frac{\text{dx}}{\sqrt{2\text{ax}-\text{x}^2}}=\text{a}^{\text{n}}\sin^{-1}\Big[\frac{\text{x}}{\text{a}}-1\Big].$ The value of n is:
→- 0
- -1
- 1
- None of these.