Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that (a) is conserved in a process (b) can never take negative values (c) must be dimensionless (d) does not vary from one point to another in space (e) has the same value for observers with different orientations of axes.

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Solution

(i)

The given statement says that scalar quantity is one that is conserved in a process. Let us take the example of kinetic energy which is a scalar quantity. It is known that kinetic energy is not conserved during inelastic collisions.

Thus, the given statement is false.

(ii)

The given statement says that scalar quantity is one that can never take negative values. Let us take the example of temperature which is a scalar quantity. It is known that temperature can take negative values.

Thus, the given statement is false.

(iii)

The given statement says that scalar quantity is one that must be dimensionless. Let us take the example of the total distance covered by an object, which is a scalar quantity. The distance covered by an object takes the dimensions of length.

Thus, the given statement is false.

(iv)

The given statement says that scalar quantity is one that does not vary from one point to another in space. Let us take the example of gravitational potential, which is a scalar quantity. It is known that, gravitational potential can vary from one point to another in space.

Thus, the given statement is false.

(v)

The given statement says that scalar quantity is one that has the same value for observers with different orientations of axes. It is known that a scalar has no direction of its own. Hence, a scalar quantity will have the same value for observers with different orientations of axes.

Thus, the given statement is true.

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Similar questions

Read each statement below carefully and state, with reasons and examples, if it is true or false :
A scalar quantity is one that ;

(a) is conserved in a process.

(b) can never take negative values

(d) does not vary from one point to another in space.

(e) has the same value for observers with different orientations of axes.

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Read each statement below carefully and state with reasons, if it is true or false:

(a) The magnitude of a vector is always a scalar, (b) each component of a vector is always a scalar, (c) the total path length is always equal to the magnitude of the displacement vector of a particle. (d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.

Read the following two statements below carefully and state, with reasons, if it is true or false.

(a) The Young’s modulus of rubber is greater than that of steel;

(b) The stretching of a coil is determined by its shear modulus.

Read each statement below carefully and state with reasons, if it is true or false :

(a) The magnitude of a vector is always a scalar,

(b) Each component of a vector is always a scalar,

(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,

(e) Three vectors not lying in a plane can never add up to give a null vector.

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