**JEE Physics Quiz Rigid Body Dynamics MCQ:** A rigid body is defined as a system of particles in which the distance between each pair of particles remains constant (with respect to time). Remember, rigid body is a mathematical concept and any system which satisfies the above condition is said to be rigid as long as it satisfies it.

**JEE Physics Quiz Rigid Body Dynamics MCQ**

A fan is running at 3000 rpm. It is switched off. It comes to rest by uniformly decreasing its angular speed in 10 seconds. The total number of revolutions in this period.

- 150
- 250
- 350
- 300

A block hangs from a string wrapped on a disc of radius 20 cm free to rotate about its axis which is fixed in a horizontal position. If the angular speed of the disc is 10 rad/s at some instant, with what speed is the block going down at that instant ?

- 4 m/s
- 3 m/s
- 2 m/s
- 5 m/s

A uniform circular disc A of radius r is made from a copper plate of thickness t and another uniform
circular disc B of radius 2r is made from a copper plate of thickness t/2. The relation between the
moments of inertia I_{A} and I_{B} is

- I
_{A}> I_{B} - I
_{A}= I_{B} - I
_{A}< I_{B} - depends on the values of t and r.

The moment of inertia of a non-uniform semicircular wire having mass m and radius r about a line perpendicular to the plane of the wire through the centre is

- mr
^{2} - 1/2 mr
^{2} - 1/4 mr
^{2} - 2/5 mr
^{2}

Let I_{A} and I_{B} be the moments of inertia of two solid cylinders of identical geometrical
shape and size
about their axes, the first made of aluminium and the second of iron.

- I
_{A}< I_{B} - I
_{A}= I_{B} - I
_{A}> I_{B} - relation between I
_{A}and I_{B}depends on the actual shapes of the bodies.

Let I_{A} and I_{B} be moments of inertia of a body about two axes 1 and 2 respectively, The
axis 1 passes
through the centre of mass of the body but axis 2 does not.

- I
_{A}< I_{B} - IF I
_{A}< I_{B}, the axes are parallel. - If the axes are parallel, I
_{A}< I_{B} - If the axes are not parallel, I
_{A}>= I_{B}

The moment of inertia of an elliptical disc of uniform mass distribution of mass ‘m’, semi major axis ‘r’, semi minor axis ‘d’ about its axis is :

- =mr
^{2}/2 - =md
^{2}/2 - >mr
^{2}/2 -
2/2

A unifrom thin rod of length L and mass M is bent at the middle point O as shown in figure. Consider an
axis passing through its middle point O and perpendicular to the plane of the bent rod. Then moment of
inertia about this axis is :

- 2/3 mL
^{2} - 1/3 mL
^{2} - 1/12 mL
^{2} - dependent on θ

The moment of inertia of a uniform circular disc about its diameter is 200 gm cm^{2}. Then its moment of
inertia about an axis passing through its center and perpendicular to its circular face is

- 100 gm cm
^{2} - 200 gm cm
^{2} - 400 gm cm
^{2} - 1000 gm cm
^{2}

A thin uniform rod of length 4l, mass 4m is bent at the points as shown in the fig. What is the moment
of inertia of the rod about the axis passing point O & perpendicular to the plane of the paper.

- ml
^{2}/3 - 10ml
^{2}/3 - ml
^{2}/12 - ml
^{2}/24

Moment of inertia of a uniform disc about the axis O O’ is:

- 3mr
^{2}/2 - mr
^{2}/2 - 5mr
^{2}/2 - 5mr
^{2}/4

The moment of inertia of a hollow cubical box of mass M and side a about an axis passing through the centres of two opposite faces is equal to

- 5ma
^{2}/3 - 5ma
^{2}/6 - 5ma
^{2}/12 - 5ma
^{2}/18

A uniform thin rod of length (4a + 2πa) and of mass (4m + 2πm) is bent and fabricated to form a square
surrounded by semicircles as shown in the figure. The moment of inertia of this frame about an axis
passing through its centre and perpendicular to its plane is

- (4 + 2π)/3 ma
^{2} - (4 + π)/3 ma
^{2} - (4 + 3π)/3 ma
^{3} - ma
^{2}{10 + 3π}/3

If a rigid body is subjected to two forces acting at (3, 3, 4) and acting at (1, 0, 0) then which of the following is (are) true?

- The body is in equilibrium.
- The body is under the influence of a torque only.
- The body is under the influence of a single force.
- The body is under the influence of a force together with a torque.

A force acts on a body at a point having position vector relative to origin of co-ordinates on the axis of rotation. The torque acting on the body about the origin is :

- 38 ˆk
- -25 ˆk
- 62 ˆk
- none of these

In case of torque of a couple if the axis is changed by displacing it parallel to itself, torque will :

- increase
- decrease
- remain constant
- None of these

Four equal and parallel forces are acting on a rod (as shown in figure) in horizontal plane at distances
of 20 cm, 40 cm, 60 cm and 80 cm respectively from one end of the rod. Under the influence of these
forces the rod :

- is at rest
- experiences a torque
- experiences a linear motion
- experiences a torque and also a linear motion

A uniform ladder of length 5m is placed against the wall in vertical plane as shown in the figure. If
coefficient of friction μ is the same for both the wall and the floor then minimum value of for it not to
slip is

- μ = 1/2
- μ = 1/4
- μ = 1/3
- μ = 1/5

A rod of weight w is supported by two parallel knife edges A & B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at a distance x from A. The normal reactions at A and B will be :

- N
_{A}= 2w (1 – x/d), N_{B}= wx/d] - N
_{A}= w (1 – x/d), N_{B}= wx/d] - N
_{A}= 2w (1 – x/d), N_{B}= 2wx/d] - N
_{A}= w (2 – x/d), N_{B}= wx/d]

The beam and pans of a balance have negligible mass. An object weighs W1 when placed in one pan and W2 when placed in the other pan. The weight W of the object is :

- √W
_{1}W_{2} - √(W
_{1}+ W_{2}) - W
_{1}^{2}+ W_{2}^{2} - (W
_{1}^{-1}+ W_{2}^{-1})/2

A uniform rod of length l is placed symmetrically on two walls as shown in figure. The rod is in
equilibrium. If N_{1} and N_{2} are the normal forces exerted by the walls on the rod then

- N
_{1}> N_{2} - N
_{1}< N_{2} - N
_{1}= N_{2} - N1 and N2 would be in the vertical directions.

A uniform circular disc A of radius r is made from a metal plate of thickness t and another uniform
circular disc B of radius 4r is made from the same metal plate of thickness t/4. If equal torques act on
the discs A and B, initially both being at rest. At a later instant, the angular speeds of a point on the rim
of A and another point on the rim of B are ω_{A} and ω_{B} respectively. We have

- ω
_{A}> ω_{B} - ω
_{A}= ω_{B} - ω
_{A}< ω_{B} - the relation depends on the actual magnitude of the torques.

A body is rotating with constant angular velocity about a vertical axis fixed in an inertial frame. The net force on a particle of the body not on the axis is

- horizontal and skew with the axis
- vertical
- horizontal and intersecting the axis
- none of these.

One end of a uniform rod having mass m and length l is hinged. The rod is placed on a smooth horizontal surface and rotates on it about the hinged end at a uniform angular velocity ω. The force exerted by the hinge on the rod has a horizontal component

- mω
^{2}l - zero
- mg
- 1/2 mω
^{2}l

The uniform rod of mass 20 kg and length 1.6 m is pivoted at its end and swings freely in the vertical
plane. Angular acceleration of rod just after the rod is released from rest in the horizontal position as
shown in figure is

- 15g/16
- 17g/16
- 16g/15
- g/15

Two men support a uniform horizontal rod at its two ends. If one of them suddenly lets go, the force exerted by the rod on the other man just after this moment will:

- remain unaffected
- increase
- decrease
- become unequal to the force exerted by him on the rod.

A uniform metre stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor assuming that the end at the floor does not slip :

- √4g
- √3g
- √5g
- √g

A uniform rod is hinged as shown in the figure and is released from a horizontal position. The angular
velocity of the rod as it passes the vertical position is: (axis is fixed, smooth and horizontal)

- √12g/3l
- √2g/3l
- √24g/7l
- √3g/7l

A constant torque acting on a uniform circular wheel changes its angular momentum from A_{0} to 4A_{0} in
4 sec. the magnitude of this torque is :

- 4A
_{0} - A
_{0} - 3A
_{0}/4 - 12A
_{0}

A particle moves with a constant velocity parallel to the Y-axis. Its angular momentum about the origin.

- is zero
- remains constant
- goes on increasing
- goes on decreasing.

A particle is projected at time t = 0 from a point P on the ground with a speed V_{0}, at an angle of 45° to
the horizontal. What is the magnitude of the angular momentum of the particle about P at time t = V_{0}/g.

- mV
_{0}^{2}/2√2g - mV
_{0}^{3}/√2g - mV
_{0}^{2}/√2g - mV
_{0}^{3}/2√2g

A uniform thin circular ring of mass ‘M’ and radius ‘R’ is rotating about its fixed axis passing through its centre perpendicular to its plane of rotation with a constant angular velocity . Two objects each of mass m, are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity.

- ωM/(M + m)
- ωM/(M + 2m)
- ωM/(M – 2m)
- ω(M + 3m)/M

A boy sitting firmly over a rotating stool has his arms folded. If he stretches his arms, his angular momentum about the axis of rotation

- increases
- decreases
- remains unchanged
- doubles

The centre of a disc rolling without slipping on a plane surface moves with speed u. A particle, on the lower half of the rim making an angle 60º with vertical, will be moving at speed

- zero
- u
- √2u
- 2u

A thin string is wrapped several times around a cylinder kept on a rough
horizontal surface. A boy standing at a distance l from the cylinder draws the
string towards him as shown in figure. The cylinder rolls without slipping. The
length of the string passed through the hand of the boy while the cylinder
reaches his hand is

- l
- 2l
- 3l
- 4l

A uniform cylinder of mass M and radius R rolls without slipping down a
slope of angle θ to the horizontal. The cylinder is connected to a spring
constant K while the other end of the spring is connected to a rigid support at
P. The cylinder is released when the spring is unstretched. The maximum
displacement of cylinder is

- 3/4 Mgsinθ/k
- Mgsinθ/k
- 2Mgsinθ/k
- 4/3 Mgsinθ/k

A system of uniform cylinders and plates is shown in figure. All the cylinders are identical and there is
no slipping at any contact. Velocity of lower & upper plate is V and 2V respectively as shown in figure.
Then the ratio of angular speed of the upper cylinders to lower cylinders is

- 3
- 1/3
- 1
- none of these

When a person throws a meter stick it is found that the centre of the stick is moving with a speed of 10 m/s vertically upwards & left end of stick with a speed of 20 m/s vertically upwards. Then the angular speed of the stick is:

- 20 rad/ sec
- 10 rad/sec
- 30 rad/sec
- none of these

As shown in the figure, a uniform disc of mass m is rolling without slipping with a angular velocity .
The portion AB is rough and BC is smooth. When it crosses point B disc will be in :

- translational motion only
- pure rolling motion
- rotational motion only
- none of these

A solid sphere, a hollow sphere and a ring, all having equal mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are equal but not sufficient to allow pure rolling. The greastest kinetic energy at the bottom of the incline will be achieved by

- the solid sphere
- the hollow sphere
- the ring
- all will achieve same kinetic energy.

A hollow sphere and a solid sphere having equal mass and equal radii are rolled down without slipping on a rough inclined plane.

- The two spheres reach the bottom simultaneously
- The hollow sphere reaches the bottom with lesser speed.
- The solid sphere reaches the bottom with greater kinetic energy
- The two spheres will reach the bottom with same linear momentum

A solid sphere, a hollow sphere and a solid cylinder, all having equal mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are equal but not sufficient to allow pure rolling. Greastest time will be taken in reaching the bottom by

- the solid sphere
- the hollow sphere
- the solid cylinder
- all will take same time.

A rough inclined plane fixed in a car accelerating on a horizontal road is shown in figure. The angle of
incline θ is related to the acceleration a of the car as a = g tanθ. If a rigid sphere is set in pure rolling on
the incline

- it will continue pure rolling
- Friction will act on it
- its angular velocity will increase
- its angular velocity will decrease.

A sphere S rolls without slipping, moving with a constant speed on a
plank P. The friction between the upper surface of P and the sphere is
sufficient to prevent slipping, while the lower surface of P is smooth and
rests on the ground. Initially, P is fixed to the ground by a pin N. If N is
suddenly removed:

- S will begin to slip on P
- P will begin to move backwards
- the speed of S will decrease and its angular velocity will increase
- there will be no change in the motion of S and P will still be at rest.

A body is given translational velocity and kept on a surface that has sufficient friction. Then:

- body will move forward before pure rolling
- body will move backward before pure rolling
- body will start pure rolling immediately
- none of these

A body of mass m and radius r is rotated with angular velocity as shown in the figure & kept on a
surface that has sufficient friction then the body will move :

- backward first and then move forward
- forward first and then move backward
- will always move forward
- none of these

A body of mass m and radius R rolling horizontally without slipping at a speed v climbs a ramp to a
height 3v^{2}/4g The rolling body can be

- a sphere
- a circular ring
- a spherical shell
- a circular disc

A sphere is released on a smooth inclined plane from the top. When it moves down its angular momentum is:

- conserved about every point
- conserved about the point of contact only
- conserved about the centre of the sphere only
- conserved about any point on a fixed line parallel to the inclined plane and passing through the centre of the ball.

A circular wooden loop of mass m and radius R rests flat on a horizontal
frictionless surface. A bullet, also of mass m, and moving with a velocity V,
strikes the loop and gets embedded in it. The thickness of the loop is much
smaller than R. The angular velocity with which the system rotates just after the
bullet strikes the loop is

- V/4R
- V/3R
- 2V/3R
- 3V/4R

A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force ‘F’ is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3a/4 above the base. The minimum value of ‘F’ for which the cube begins to tilt about the edge is (assume that the cube does not slide)

- 2/3 mg
- 4/3 mg
- 5/4 mg
- 1/2 mg

A homogenous block having its cross-section to be a parallelogram of sides ‘a’ and ‘b’ (as shown) is
lying at rest and is in equilibrium on a smooth horizontal surface. Then for acute angle θ:

- cosθ <= b/a
- cosθ >= b/a
- cosθ < b/a
- cosθ > b/a
- cosθ > a/b

An equilateral uniform prism of mass m rests on a rough horizontal surface with coefficient of friction .
A horizontal force F is applied on the prism as shown in the figure. If the coefficient of friction is
sufficiently high so that the prism does not slide before toppling, then the minimum force required to
topple the prism is :

- mg/√3
- mg/4
- μmg/√3
- μmg/4