Motion in a Plane
© examsnet.com
Question : 4
Total: 32
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful :
(a) adding any two scalars.
(b) adding a scalar to a vector of the same dimensions.
(c) multiplying any vector by any scalar.
(d) multiplying any two scalar.
(e) adding any two vectors.
(f) adding a component of a vector to the same vector.
(a) adding any two scalars.
(b) adding a scalar to a vector of the same dimensions.
(c) multiplying any vector by any scalar.
(d) multiplying any two scalar.
(e) adding any two vectors.
(f) adding a component of a vector to the same vector.
Solution:
(a) No, adding any two scalars is not meaningful because only thescalars of same dimensions (i.e. of same nature) can be added.
(b) No, adding a scalar to a vector of the same dimension is notmeaningful because a scalar cannot be added to a vector.
(c) Yes, multiplying any vector by any scalar is meaningful algebraicoperation. It is because when any vector is multiplied by any scalar,then we get a vector having magnitude equal to scalar number times the magnitude of the given vector. e.g. when acceleration a is multiplied bymass m, we get force F = ma which is a meaningful operation.
(d) Yes, the product of two scalars gives a meaningful result e.g. whenpower P is multiplied by time t, then we get work done (W) i.e. W = Pt,which is a meaningful algebraic operation.
(e) No, as the two vectors of same dimensions (i.e. of the same nature)can only be added, so addition of any two vectors is not a meaningfulalgebraic operation.
(f) No, a component of a vector can be added to the same vector only byusing the law of vector addition. So, the addition of a vector to the samevector is not a meaningful operation.
(b) No, adding a scalar to a vector of the same dimension is notmeaningful because a scalar cannot be added to a vector.
(c) Yes, multiplying any vector by any scalar is meaningful algebraicoperation. It is because when any vector is multiplied by any scalar,then we get a vector having magnitude equal to scalar number times the magnitude of the given vector. e.g. when acceleration a is multiplied bymass m, we get force F = ma which is a meaningful operation.
(d) Yes, the product of two scalars gives a meaningful result e.g. whenpower P is multiplied by time t, then we get work done (W) i.e. W = Pt,which is a meaningful algebraic operation.
(e) No, as the two vectors of same dimensions (i.e. of the same nature)can only be added, so addition of any two vectors is not a meaningfulalgebraic operation.
(f) No, a component of a vector can be added to the same vector only byusing the law of vector addition. So, the addition of a vector to the samevector is not a meaningful operation.
© examsnet.com
Go to Question: