Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv)
cube, each of uniform mass density. Does the centre of mass of a body necessarily lie
inside the body ?
Slowing down of neutrons:
In a nuclear reactor a neutron of high
speed (typically 107
m s–1) must be slowed
to 103
m s–1 so that it can have a high
probability of interacting with isotope 92
235U
and causing it to fission. Show that a
neutron can lose most of its kinetic energy
in an elastic collision with a light nuclei
like deuterium or carbon which has a mass
of only a few times the neutron mass. The
material making up the light nuclei, usually
heavy water (D2O) or graphite, is called a
moderator.
Consider Example 5.8 taking
the coefficient of friction, µ, to be 0.5 and
calculate the maximum compression of the
spring.
To simulate car accidents, auto
manufacturers study the collisions of moving
cars with mounted springs of different spring
constants. Consider a typical simulation with
a car of mass 1000 kg moving with a speed
18.0 km/h on a smooth road and colliding
with a horizontally mounted spring of spring
constant 5.25 × 10
3
N m–1
. What is the
maximum compression of the spring ?
A bob of mass m is suspended
by a light string of length L . It is imparted a
horizontal velocity vo
at the lowest point A
such that it completes a semi-circular
trajectory in the vertical plane with the string
becoming slack only on reaching the topmost
point, C. This is shown in Fig. 5.6. Obtain an
expression for (i) vo
; (ii) the speeds at points
B and C; (iii) the ratio of the kinetic energies
(KB
/KC
) at B and C. Comment on the nature
of the trajectory of the bob after it reaches
the point C.
A block of mass m = 1 kg,
moving on a horizontal surface with speed
vi
= 2 m s–1 enters a rough patch ranging
from x = 0.10 m to x = 2.01 m. The retarding
force Fr
on the block in this range is inversely
proportional to x over this range,
F
k
x
r =
−
for 0.1 < x < 2.01 m
= 0 for x < 0.1m and x > 2.01 m
where k = 0.5 J. What is the final kinetic
energy and speed vf
of the block as it
crosses this patch ?
A woman pushes a trunk on
a railway platform which has a rough
surface. She applies a force of 100 N over a
distance of 10 m. Thereafter, she gets
progressively tired and her applied force
reduces linearly with distance to 50 N. The
total distance through which the trunk has
been moved is 20 m. Plot the force applied
by the woman and the frictional force, which
is 50 N versus displacement. Calculate the
work done by the two forces over 20 m.
In a ballistics demonstration
a police officer fires a bullet of mass 50.0 g
with speed 200 m s-1 (see Table 5.2) on soft
plywood of thickness 2.00 cm. The bullet
emerges with only 10% of its initial kinetic
energy. What is the emergent speed of the
bullet ?
A cyclist comes to a skidding
stop in 10 m. During this process, the force
on the cycle due to the road is 200 N and
is directly opposed to the motion. (a) How
much work does the road do on the cycle ?
(b) How much work does the cycle do on
the road ?
It is well known that a
raindrop falls under the influence of the
downward gravitational force and the
opposing resistive force. The latter is knownto be proportional to the speed of the drop
but is otherwise undetermined. Consider
a drop of mass 1.00 g falling from a height
1.00 km. It hits the ground with a speed of
50.0 m s-1. (a) What is the work done by the
gravitational force ? What is the work done
by the unknown resistive force?
+91 94284 01196 (WhatsApp only)
C-15, Suvidhapark Society, Amitnagar circle, Karelibaug, Vadodara (390018)
© Copyright 2025. Doubtora. All Rights Reserved
