On an open ground, a motorist follows a track that turns to his left by an angle of 600
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.
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P
of the park, then cycles along the circumference, and returns to the centre along QO
as shown in Fig. 3.20. If the round trip takes 10 min, what is the (a) net displacement,
(b) average velocity, and (c) average speed of the cyclist ?
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 ?
Establish the following vector inequalities geometrically or otherwise :
(a) |a+b| < |a| + |b|
(b) |a+b| > ||a| −|b||
(c) |a−b| < |a| + |b|
(d) |a−b| > ||a| − |b||
When does the equality sign above apply?
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.
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.
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.
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.
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.
Reaction time : When a
situation demands our immediate
action, it takes some time before we
really respond. Reaction time is the
time a person takes to observe, think
and act. For example, if a person is
driving and suddenly a boy appears on
the road, then the time elapsed before
he slams the brakes of the car is the
reaction time. Reaction time depends
on complexity of the situation and on
an individual.
You can measure your reaction
time by a simple experiment. Take a
ruler and ask your friend to drop it
vertically through the gap between
your thumb and forefinger (Fig. 2.8).
After you catch it, find the distance d
travelled by the ruler. In a particular
case, d was found to be 21.0 cm.
Estimate reaction time.
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