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प्रश्न
Read the statement below carefully and state, with reason and example, if it is true or false:
A scalar quantity is one that must be dimensionless.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
There are numerous scalar quantities that are not dimensionless. For example, scalar quantities like mass, density, and charge all have dimensions.
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संबंधित प्रश्न
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
- adding any two scalars,
- adding a scalar to a vector of the same dimensions,
- multiplying any vector by any scalar,
- multiplying any two scalars,
- adding any two vectors,
- adding a component of a vector to the same vector.
Read the statement below carefully and state with reason, if it is true or false:
Three vectors not lying in a plane can never add up to give a null vector.
A vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors a and b at different locations in space necessarily have identical physical effects? Give examples in support of your answer.
Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain.
Which one of the following statements is true?
The angle between A = `hati` + `hatj` and B = `hati` − `hatj` is ______.
Three vectors A, B and C add up to zero. Find which is false.
It is found that |A + B| = |A|.This necessarily implies ______.
Following are four differrent relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s):
- `v_(av) = 1/2 [v(t_1) + v(t_2)]`
- `v_(av) = (r(t_2) - r(t_1))/(t_2 - t_1)`
- `r = 1/2 (v(t_2) - v(t_1))(t_2 - t_1)`
- `a_(av) = (v(t_2) - v(t_1))/(t_2 - t_1)`
If |A| = 2 and |B| = 4, then match the relations in column I with the angle θ between A and B in column II.
| Column I | Column II |
| (a) A.B = 0 | (i) θ = 0 |
| (b) A.B = + 8 | (ii) θ = 90° |
| (c) A.B = 4 | (iii) θ = 180° |
| (d) A.B = – 8 | (iv) θ = 60° |
