System of Particles and Rotational Motion
Q 1 Two masses m1 and m2 start moving towards each other due to their mutual force of
attraction. What will be the change in their respective centre of mass position?
Mark (1)
View Answer
Q 2 What is the S.I. unit of angular momentum?
Mark (1)
View Answer
Q 3 Is radius of gyration of a body a constant quantity?
Mark (1)
View Answer
Q 4 Where is the centre of mass of a uniform cube located?
Mark (1)
View Answer
Q 5 A solid sphere and a hollow sphere having same density and radius are rolling down
an inclined plane. Which one of them will reach first?
Mark (1)
View Answer
Q 6 Where is the centre of mass of a system of two particles is situated?
Mark (1)
View Answer
Q 7 In which situation, centre of mass has no acceleration?
Mark (1)
View Answer
Q 8 Two particles of masses 1 gm and 2 gm are at distance 1 m apart.Find their centre of
mass.
Mark (1)
View Answer
Q 9 A child starts running from one end to another end of a trolley which is moving with
uniform speed V on a smooth horizontal floor. What is the speed of the C.M. of the
(trolley+ child) system?
Marks (2)
View Answer
Q 10 Find the moment of inertia of a solid sphere about a tangent to the sphere.
Marks (2)
View Answer
Q 11 Prove that the torque experienced by a particle is equal to the product of its moment
of inertia and angular acceleration.
Marks (2)
View Answer
Q 12 A solid cylinder of mass 20 kg rotates on its axis with angular speed 100 rad s-1.The
radius of the cylinder is 0.25 m.What is the kinetic energy associated with the rotation of
the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
Marks (2)
View Answer
Q 13 A rope of negligible mass is wound over a hollow cylinder of mass 4 kg and radius
27 cm.What is the angular acceleration of the cylinder if the rope is pulled with a force of
30N? What is the linear acceleration of the rope?
Marks (2)
View Answer
Q 14 What do you mean by conservation of linear momentum?
Marks (2)
View Answer
Q 15 A bullet of mass 50 g and speed 500 m/sec gets embedded exactly at the centre of
the door. If the door is 1 m wide and weighs 12 kg, find the angular speed of the door just
after the bullet embedded into it?
Marks (2)
View Answer
Q 16 Find the moment of inertia of a rod of length l about an axis passing through its mid
point and perpendicular to it?
Marks (3)
View Answer
Q 17 A man of mass m1 is standing on a platform of mass m2 kept on a smooth horizontal
surface. The man starts moving on the platform with a velocity Vr relative to the
platform. Find the recoil velocity of the platform.
Marks (3)
View Answer
Q 18 A uniform chain of length 3 m is kept on a table such that a length of 40 cm hangs
freely from the edge of the table. The total mass of the chain is 4 kg.What is the work
done in pulling the entire chain on the table?
Marks (3)
View Answer
Q 19
What is the S.I. unit of angular momentum?
Marks (4)
View Answer
Q 20
Two particles of masses 1 gm and 2gm are at distance 1 m apart.Find their centre of
mass.
Marks (4)
View Answer
Q 21 Prove that the torque experienced by a particle is equal to the product of its moment
of inertia and angular acceleration.
Marks (4)
View Answer
Q 22
A solid cylinder of mass 20 kg rotates on its axis with angular speed 100 rad s-1.The
radius of the cylinder is 0.25m.What is the kinetic energy associated with the rotation of
the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
Marks (4)
View Answer
Q 23
A rope of negligible mass is wound over a hollow cylinder of mass 4kg and radius
27cm.What is the angular acceleration of the cylinder if the rope is pulled with a force of
30N? What is the linear acceleration of the rope?
Marks (4)
View Answer
Q 24
What do you mean by conservation of linear momentum?
Marks (4)
View Answer
Q 25
A bullet of mass 50g and speed 500m/sec gets embedded exactly at the centre of the
door. If the door is 1m wide and weighs 12kg find the angular speed of the door just after
the bullet embedded into it?
Marks (4)
View Answer
Q 26 A particle traverses its circular path as = 2t2 + t where,
centre in radian and t is time in seconds. Find
is the angle made at the
(a) angular displacement at t = 2 s
(b) angular velocity at t = 2 s
(c) angular acceleration
(d) tangential acceleration at t = 1s if radius of circle is 5 m.
Marks (5)
View Answer
Q 27 A wheel is resting about its axis(fixed).A constant force of 10 N is applied
tangentially to the wheel. Find the angular displacement made after one second. Also find
angular speed after one revolution. Mass of the wheel is 10 kg and radius is 0.5 m.
Marks (5)
View Answer
Q 28 Two blocks of masses m1 and m2 are connected by string (massless and frictionless)
passing over rough pulley(mass m and radius r).If the system is released, then find the
acceleration of masses m1 and m2 and tension in the string. There is no friction between
m2 and surface. There is no sliding between pulley and string.
Marks (5)
View Answer
Q 29 A sphere of mass m and radius r rolls without slipping on inclined plane of
inclination .Find the linear acceleration of the system and force of friction acting on it.
What should be the minimum coefficient of static friction to support pure rolling?
Marks (5)
View Answer
Q 30 State and prove perpendicular axes theorem.
Marks (5)
View Answer
Q 31 A solid sphere rolls up an inclined plane of angle of inclination 300.At the bottom of
the inclined plane the centre of mass of the sphere has speed of 5 m/sec.Find how far up
the sphere will go?
Marks (5)
View Answer
Q 32 Two masses m1 and m2 are separated by distance r. Find the moment of inertia of
this arrangement about an axis passing through the centre of mass and perpendicular to
the line joining them.
Marks (5)
View Answer
Q 33 A solid sphere rolls down an inclined plane of inclination
it reached the bottom of the inclined plane?
Marks (5)
View Answer
. Find its velocity when