Class- XI
Subject - Physics
ROTATIONAL
MOTION
Q.1When a man jumps out of a boat, the boat tends to
move in the backward direction. Explain this phenomena on the basis of
(a) Concept
of center of mass
(b) Newton’s
third law
(c) Conservation
of momentum
Q.2A particle of mass 5kg is kept at the point 2i + 3j
+ 7k. Another particle of mass 3kg is kept at the point having position vector
5i – 7j –k. Find the position vector of the CoM. If no external force is acting
on the system, how would the position of CoM change?
Q.3 A particle “P” having mass 1kg is moving with a
velocity of 3i + 7j m/s. Another particle “Q” of mass 2kg is moving with a
velocity of 6j – k m/s. Find the velocity of CoM. How would the velocity of CoM
change if no external force is acting on the system?
Q.4> Using the method of integration derive the moment of
inertia for following mass distributions
(a) Thin
rod of mass M and length L rotating about an axis through the CoM
(b) Thin
rod of mass M and length L rotating about an axis passing through one of its
ends
(c) Circular
ring of mass M and radius R
(d) Circular
disc of mass M and radius R
Q.5> Explain why earth and moon revolve around their
common center of mass. Draw suitable figure
Q.6> What is center of gravity? How is it different from
center of mass?
Q.7> A fan has a moment of inertia of 10kgm2.
After being switched on, it attains a speed of 240rpm in
10 seconds. What is the torque provided by the motor? What
is the work done by the motor in bringing the fan to this speed?
Q.8> The radius of the wheels of a bike is 25cm. On
acceleration, the bike can reach a speed of
72kmph in just 6 seconds. What is the torque produced by the
engine?
Q.9> A force F = 4i + 7j – 2k acts on a particle whose
position vector is r = 6i – j + 3k. The particle is free to rotate about an
axis passing through the origin. Find the torque produced by the force.
Q.10> To maintain a fan at a constant speed of 10rad/sec
the motor has to provide a torque of 100Nm. Explain why this torque is required
for maintaining a constant speed. What is the power delivered by the motor?
Q.11> A torque of 10Nm acts on a ring of mass 2kg and
radius 1m. Find the angle through which the ring will rotate in 5 seconds. What
is the final angular velocity?
(b) Using two different approaches, find the amount of work
done by the applied torque.
Q.12> Define a
couple. Two equal and opposite forces of 50N are acting at the opposite end of
a rod of length 1m. What is the net torque and net force?
Q.13 The length of a boat is 10m and its mass is 100kg.
A person of mass 50kg is standing at the left corner. As the person moves
towards the right, the boat starts drifting towards the left. Explain why ??
The person moves a total of 5m with respect to the boat. By
how much would the boat drift?
Q.14>A solid sphere is rolling on the horizontal
surface. What fraction of its total kinetic energy is associated with its
rotational motion.
Q.15>A solid cylinder of mass M and radius R is kept on
a rough inclined plane of inclination θ and is allowed to roll down. Find its
acceleration and the force of friction acting on it. What is the minimum
coefficient of friction required for pure rolling to take place?
Q.16>Draw a table showing the analogy b/w linear motion
and rotational motion.
Q.17>Explain how the knowledge of conservation of
angular momentum is useful to a diver.
Q.18 A body “P” having mass 5kg is kept at x = 2.
Another body “Q” of mass 10ks is kept at x = 8. Due to their mutual force of
gravitational attraction they start moving towards each other. Find the
position at which they will collide.
Q.19 What is radius of gyration. Mention its units and
dimension.
Q.20 A wheel of mass M is rotating with a constant
angular velocity of ω. Two particles of mass m each are attached to its corner.
How does this affect the angular velocity?
Q.21 The density of a rod varies as d = 10 – 5x. The
length of the rod is 1m. Find its moment of inertia about an axis passing
through one of the ends ( x = 0 )
Q.22 A boat is 20m wide and its mass is 500kg. A person
of mass 100kg is standing at the center. As the person moves towards the right,
the boat starts drifting towards the left. The person continues moving towards
the right till he reaches the end. Find
(a) By
how much would the boat drift?
(b) What
is the actual displacement of the person.
Q.23 Mention the units and dimension of the following
quantities.
(a) Torque
(b) Moment
of inertia
(c) Angular
momentum
(d) Angular
impulse
(e) Rotational
kinetic energy
Q.24 A radius of the wheels of a car is 20cm. The car is
moving with a constant velocity of 10m/s. The maintain the rotation of the
wheels, the engine has to deliver a torque of 125Nm. What is the power of the
engine?
25 A rod of length 5m is supported by two strings as shown in
the figure. It is made of a material of non-uniform density
because
of which the center of mass does not lie at the geometrical
center.
The rod is in a position of equilibrium, translational as
well as
rotational. This means that the net force as well as the net
torque
acting on it are zero. Find the position of CoM
(b) In which of the
ropes is the tension greater?
(c) The
same rod is now suspended by two vertical strings. Find the tension in both the
strings. The mass of the rod is 4kg
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