A car moving along a straight highway with speed of 126 km h–1 is brought to a
stop within a distance of 200 m. What is the retardation of the car (assumed
uniform), and how long does it take for the car to stop ?
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward,
followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m
long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and
otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
A woman starts from her home at 9.00 am, walks with a speed of 5 km h–1 on a
straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and
returns home by an auto with a speed of 25 km h–1. Choose suitable scales and
plot the x-t graph of her motion.
The position-time (x-t) graphs for two children A and B returning from their school
O to their homes P and Q respectively are shown in Fig. 2.9. Choose the correct
entries in the brackets below ;
(a) (A/B) lives closer to the school than (B/A)
(b) (A/B) starts from the school earlier than (B/A)
(c) (A/B) walks faster than (B/A)
(d) A and B reach home at the (same/different) time
(e) (A/B) overtakes (B/A) on the road (once/twice).
In which of the following examples of motion, can the body be considered
approximately a point object:
(a) a railway carriage moving without jerks between two stations.
(b) a monkey sitting on top of a man cycling smoothly on a circular track.
(c) a spinning cricket ball that turns sharply on hitting the ground.
(d) a tumbling beaker that has slipped off the edge of a table.
Consider a simple
pendulum, having a bob attached to a
string, that oscillates under the action of
the force of gravity. Suppose that the period
of oscillation of the simple pendulum
depends on its length (l), mass of the bob
(m) and acceleration due to gravity (g).
Derive the expression for its time period
using method of dimensions.
Example 1.4 The SI unit of energy is
J = kg m2 s
–2; that of speed v is m s–1 and
of acceleration a is m s–2. Which of the
formulae for kinetic energy (K) given below
can you rule out on the basis of
dimensional arguments (m stands for the
mass of the body) :
(a) K = m2
v3
(b) K = (1/2)mv2
(c) K = ma
(d) K = (3/16)mv2
(e) K = (1/2)mv2 + ma
Let us consider an equation
1
2
m v m g h 2
=
where m is the mass of the body, v its
velocity, g is the acceleration due to
gravity and h is the height. Check
whether this equation is dimensionally
correct.
5.74 g of a substance
occupies 1.2 cm3
. Express its density by
keeping the significant figures in view.
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