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.
Stopping distance of
vehicles : When brakes are applied to a
moving vehicle, the distance it travels before
stopping is called stopping distance. It is
an important factor for road safety and
depends on the initial velocity (v0
) and the
braking capacity, or deceleration, –a that
is caused by the braking. Derive an
expression for stopping distance of a vehicle
in terms of vo
anda.
Galileo’s law of odd
numbers : “The distances traversed, during
equal intervals of time, by a body falling
from rest, stand to one another in the same
ratio as the odd numbers beginning with
unity [namely, 1: 3: 5: 7……].” Prove it.
+91 94284 01196
© Copyright 2025. Doubtora. All Rights Reserved
