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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

Read each statement below carefully and state with reasons, if it is true or false:
(a) The magnitude of 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 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.

(a)True, because magnitude is a pure number. 

(b)  False, each component of a vector is always a vector, not a scalar.

(c) False, total path length can also be more than the magnitude of displacement vector of a particle. e.g. when a particle follows the arc of circle, the length of path is greater than magnitude of the displacement.

This statement is true only if the particle is moving in a straight line. 

(d) True, because the total path length is either greater than or equal to the magnitude of the displacement vector. 

(e) True, as the three vectors cannot be represented by the three sides of a triangle taken in the same order. 

209 Views

Pick out the two scalar quantities in the following list:

force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.

Work and current are scalar quantities.


The dot product of force and displacement gives us the amount of work done. And, we know that the dot product of two quantities is always a scalar. Therefore, work is a scalar physical quantity.

Current is described only by its magnitude. Its direction is not taken. Hence, it is a scalar quantity.
152 Views

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.

(a) False -  When we carry out the adiabatic process, the scalar quantity temperature does not conserve.

In inelastic collisions, the K.E. (scalar quantity) does not conserve.

(b) False - scalar quantity can have negative value e.g. <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre>.

If the angle between <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre> is greater than 90 degree commathen W will be negative e.g. work done by gravitational force when body is raised upward is negative.

(c) False -  Scalar quantity may have dimensions, e.g. Dimensional formula of work is [M1L2T-2].

(d) False - Temperature is a scalar quantity and it changes as we go higher, the gravitational potential is a scalar quantity and it varies with the height.

(e) True.
152 Views

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 scalars,
(e) adding any two vectors,
(f) adding a component of a vector to the same vector.


(a)  If the scalars are similar type of quantities, adding of scalars will be meaningful. Scalars of the same dimension can only be added. 

(b) Adding a scalar to a vector of the same dimension is meaningless. a scalar cannot be added to a vector. 

(c) Any vector can be multiplied by a scalar. A vector when multiplied by a scalar quantity will give us a vector quantity. When the vector quantity acceleration is multiplied by m, we get a force, straight F with rightwards harpoon with barb upwards on top space equals space m a, which is a meaningful operation.

(d) Two scalars can be multiplied together. For example, when power is multiplied by time t, we get the quatity, work done. 

(e) Adding any two vectors is meanigless because two vectors of the same dimnsion can be added.

(f) Adding a component of a vector to the same vector is meaningful. Because both the vectors are of the same dimensions.

303 Views

A cyclist starts from the center O of circle of park of radius 1 km, reaches the edge P of the park, then cycles along the circumference to point Q and returns to the centre along QO as shown. If the round trip takes 10 minutes, then what is:

(a) net displacement
(b) average velocity
(c) average speed of the cyclist?

(a) The cyclist starts from O and again returns to point O. Therefore, the initial and the final point are the same. Hence, displacement of cyclist is equal to zero.

(b) Average velocity of cyclist is zero because total displacement of cyclist is zero.

(c) Total distance travelled by cyclist is,

             straight S equals OP plus PQ with overparenthesis on top plus QO

               equals straight r plus πr over 2 plus straight r equals straight r open parentheses fraction numerator 4 plus straight pi over denominator 2 end fraction close parentheses 

∴      Average speed  = straight S over straight t equals open parentheses fraction numerator 4 plus straight pi over denominator 2 end fraction close parentheses straight r over straight t

Here, we have

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and

Time taken for round trip,space space space straight t equals 10 min equals 600 straight s

∴  Average space speed space equals space open parentheses fraction numerator 4 plus straight pi over denominator 2 end fraction close parentheses 1000 over 600 

                        space space equals 5.95 space straight m divided by straight s 

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