Look at the graphs (a) to (d) Figure carefully and state, with reasons, which of these *cannot *possibly represent one-dimensional motion of a particle.

Concept: Position, Path Length and Displacement

Fill in the blanks by suitable conversion of units: 1 kg m^{2}s^{–2}= ....g cm^{2} s^{–2}

Concept: International System of Units

Fill in the blanks by suitable conversion of units

1 m =..... ly

Concept: Position, Path Length and Displacement

Fill in the blanks by suitable conversion of units:

3.0 m s^{–2}=.... km h^{–2}

Concept: International System of Units

Fill in the blanks by suitable conversion of units:

G= 6.67 × 10^{–11} N m^{2} (kg)^{–2}=.... (cm)^{3}s^{–2} g^{–1}.

Concept: International System of Units

State the number of significant figures in the following:

2.64 × 10^{24} kg

Concept: Position, Path Length and Displacement

Figure shows the *x-t *plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for *t *< 0 and on a parabolic path for *t *> 0? If not, suggest a suitable physical context for this graph.

Concept: Position, Path Length and Displacement

A police van moving on a highway with a speed of 30 km h^{–1} fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h^{–1}. If the muzzle speed of the bullet is 150 m s^{–1}, with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Concept: Position, Path Length and Displacement

State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

Concept: Scalars and Vectors

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.

Concept: Scalars and Vectors

Pick out the only vector quantity in the following list:

Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

Concept: Scalars and Vectors

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.

Concept: Scalars and Vectors

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

The magnitude of a vector is always a scalar

Concept: Scalars and Vectors

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

Each component of a vector is always a scalar

Concept: Scalars and Vectors

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

the total path length is always equal to the magnitude of the displacement vector of a particle.

Concept: Scalars and Vectors

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

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

Concept: Scalars and Vectors

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

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

Concept: Scalars and Vectors

Given **a ****+ ****b ****+ ****c ****+ ****d ****= ****0**, which of the following statements are correct:

(a) **a****, ****b****, ****c****, **and **d **must each be a null vector,

(b) The magnitude of (**a ****+ ****c**) equals the magnitude of (**b****+ ****d**),

(c) The magnitude of *a *can never be greater than the sum of the magnitudes of **b***, ***c**, and **d***,*

(*d*) **b ****+ ****c **must lie in the plane of **a** and **d **if **a** and **d **are not collinear, and in the line of **a **and **d**, if they are collinear?

Concept: Scalars and Vectors

Three girls skating on a circular ice ground of radius 200 m start from a point Pon the edge of the ground and reach a point Qdiametrically opposite to P following different paths as shown in Figure. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?

Concept: Scalars and Vectors

On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Concept: Scalars and Vectors