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Which of the following is unitless quantity?
- a)Pressure gradient
- b)Displacement gradient
- c)Force gardient
- d)Velocity gradient
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Which of the following is unitless quantity?a)Pressure gradientb)Displ...
Among the given quantities displacement gradient is a unitless quantity.
Most Upvoted Answer
Which of the following is unitless quantity?a)Pressure gradientb)Displ...
Displacement gradient is the correct answer.
Explanation:
- Displacement gradient is a measure of the change in displacement per unit length in a given direction.
- It is a measure of how much an object has moved or been displaced with respect to its original position.
- Displacement is a distance quantity, which means it has units of length (such as meters or centimeters).
- However, displacement gradient is a ratio of two lengths, and the units cancel out, leaving a unitless quantity.
Examples:
- Suppose we have a rod that is 10 meters long, and we apply a force that causes the rod to stretch by 2 meters. The displacement gradient would be 2 meters divided by 10 meters, which equals 0.2. The unit of meters cancels out, leaving a unitless quantity.
Other options:
- Pressure gradient: Pressure is force per unit area, so pressure gradient has units of force per unit area. It is not a unitless quantity.
- Force gradient: Force is a vector quantity, and its gradient would also be a vector quantity. It is not a unitless quantity.
- Velocity gradient: Velocity is a vector quantity, and its gradient would also be a vector quantity. It is not a unitless quantity.
Therefore, the unitless quantity among the given options is the displacement gradient.
Explanation:
- Displacement gradient is a measure of the change in displacement per unit length in a given direction.
- It is a measure of how much an object has moved or been displaced with respect to its original position.
- Displacement is a distance quantity, which means it has units of length (such as meters or centimeters).
- However, displacement gradient is a ratio of two lengths, and the units cancel out, leaving a unitless quantity.
Examples:
- Suppose we have a rod that is 10 meters long, and we apply a force that causes the rod to stretch by 2 meters. The displacement gradient would be 2 meters divided by 10 meters, which equals 0.2. The unit of meters cancels out, leaving a unitless quantity.
Other options:
- Pressure gradient: Pressure is force per unit area, so pressure gradient has units of force per unit area. It is not a unitless quantity.
- Force gradient: Force is a vector quantity, and its gradient would also be a vector quantity. It is not a unitless quantity.
- Velocity gradient: Velocity is a vector quantity, and its gradient would also be a vector quantity. It is not a unitless quantity.
Therefore, the unitless quantity among the given options is the displacement gradient.
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Which of the following is unitless quantity?a)Pressure gradientb)Displacement gradientc)Force gardientd)Velocity gradientCorrect answer is option 'B'. Can you explain this answer?
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