Motion in A Plane

Physics Part I

Physics

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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, , 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.

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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 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. .

If the angle between is greater than then 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 [M

(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.

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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) 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.

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(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,

∴ Average speed =

Here, we have

Radius of the circle park,

and

Time taken for round trip,

∴

145 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.

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