#### In case of a cone of height 'h', the height of its centre of mass from its base is ____ if the cone is hollow and ____ if the cone is solid.

For a hollow cone, the C.M. is at a height of h/3 from the base and for a solid cone, the centre of mass is at a height of h/4.

#### (a) When a top is rotating, magnitude of its angular velocity may change but its direction remains the same.

Angular acceleration is a vector quantity.

The direction of angular velocity remains the same for a body rotating about fixed axis. In case of a rotating top, the motion is known as 'Precession' where the axis of the top moves around a vertical. Angular acceleration is a vector quantity.

#### Torque due to weight of a body about its centre of gravity is ____.

Torque due to weight of a body about its centre of gravity is zero.

#### ____ is not an example of a rigid body in pure rotational motion

Rotating top, rotating fan and rotating wheel all are in pure rotational motion. The earth exhibits both rotational and translational motions.

#### The ratio of angular speeds of minute hand and second hand of a clock is ____.

A minute hand makes one rotation in one hour. That means its angular speed is "one rotation per hour".

A seconds hand takes one minute to make one rotation that means, it makes sixty rotations in one hour. Its angular speed is "sixty rotations in one hour".

The ratio of angular speed of minute hand and second hand of a clock is 1: 60.

#### When a rigid body is in motion, it is observed that all its particles have equal velocities. The motion of the rigid body is ____

If a rigid body is in pure translational motion; all particles of the body will have same velocities.

#### In rotational motion of a rigid body "rotation about a fixed axis" can be compared with ____ of translational motion.

Rotation about a fixed axis is a special case of rotational motion that can be compared with motion with uniform acceleration at transnational work.

#### A circular ring of mass 'M' and radius 'R' is suspended from a nail. The moment of inertia of the ring about an axis passing through the nail is ____.

For a ring moment of inertia about an axis passing through the center and perpendicular to the plane is I_{C} = MR^{2}
The axis passing through the nail is parallel to this and is at a distance 'R' from the earlier axis.
I = I_{C} + MR^{2} = MR^{2} + MR^{2 }= 2MR^{2}

#### When a particle is moving along a circular path with uniform speed. ____ remains constant both in magnitude and direction.

When a particle is moving along a circular path with uniform speed. The magnitudes of its linear velocity, centripetal acceleration and centripetal force is constant but their directions change continuously. As for angular velocity, both its magnitude and direction remains constant.

#### Centre of mass of a system of particles is a point in space that ____.

Centre of mass of a rigid body or a system of particles is a point in space that may or may not coincide with the geometric centre of the body or system.

#### The centre of gravity of a 5 kg mass is located at (4, 5). If g = 10 m/ s^{2}, torque of weight about the origin is ____. Weight of the body acts along -y direction.

Torque of weight = weight × perpendicular distance of line passing through the centre of gravity = 5 × 10 × 4 = 200 Nm.

#### The centre of mass of a system of particles all lying along x-axis is located ____.

Since all particles of the system lie along x-axis, the centre of mass of the system of particles also is located on x-axis.

#### The moment of inertia of a solid cylinder about its axis ____ with increase in temperature.

When temperature of the cylinder is increases, it expands and more mass is distributed at larger distances. As a result, the moment of inertia increases.

#### The dimensions of____ is not ML^{2}T^{−2}.

Work and energy do have dimensions similar to that of torque and are ML^{2}T^{−2}. Only power has different dimensions. ML^{2}T^{−3}.

#### Angular velocity of the earth rotating about its axis is ω_{E}, angular velocity of hour's hand of a clock is ω_{h}, angular velocity of seconds hand of a clock is ω_{s}, and angular velocity of a disc making 25 rpm is ω_{d } then ____.

The earth makes one rotation per 24 hours. ω_{E} =1/24rph.

Hour's hand of a clock takes 12 hours to make one rotation ω_{h}=1/12rph.

Seconds hand of a clock takes one minute to make one rotation. Hence ω_{s} = 60 rph.

Angular velocity of disk ω_{d} = 25 rpm = 25 × 60 rph.

So, ω_{E}<ω_{h}<ω_{s}<ω_{d}.

#### A flywheel is of diameter 0.2 m is rotating about its axis. If a point on the edge has a linear speed of 10 m/s, the angular speed of the flywheel is ____.

v = ωr or ω = v/r = (10m/s)/(0.1)=100 rad/s

#### When a rigid body rotates about a fixed axis ____ with time.

For a rotation about a fixed axis, the directions of the vector 'ω' does not change but its magnitude may change with time.

#### (a) When a body is in pure translational motion, all points of the body have the same linear velocity at any instant of time.

(b) When a rigid body is in pure rotational motion, all points of the body have the same angular velocity.

When in pure translational all points have the same linear velocity and when in pure rotational motion, all points have the same angular velocity.

#### When the reference frame is attached to the centre of mass, the motion of a spinning cricket ball is ____

In general motion of any rigid body can be considered as a combination of "translational motion of its centre of mass" and rotational motion of all other parts of the body about its centre of mass. When the frame of reference is attached to the centre of mass of the cricket ball, the only motion one can observe is the rotation of other particles of the ball about its centre of mass. Hence, the motion looks to be pure rotational.

#### When a car is in motion, the nature of motion of its wheels is ____

The motion of wheels is rolling motion which can be considered as a combination of translational and rotational motions.

#### When a door is pushed near the edge the torque acting is "τ". If the same force is acting at the middle of the door, the torque acting is ____. (Assume that the force is acting perpendicular in both the cases).

T = r × F

When force is same, T α r

If the force is acting at half the distance it was acting earlier the torque also must be half of the earlier value. Hence the new torque must be "T/2".

#### "A" and "B" are two particles of a cricket ball separated by a small distance of 0.01 m. A spinner bowls it with a speed of 80 km/h. Just before it was hit by a batsman, the distance between "A" and "B" is ___

For a rigid body the distance between all pairs of particles does not change as the body is in motion.

#### ____ is an example of a rigid body in pure translational motion.

The motion of a spinning top and a rolling sphere represents a combination of translational and rotational motions. Only the sphere sliding over the inclined plane exhibits pure translational motion.

#### The time rate of angular momentum of a system of particles about a point is equal to the sum of the external torques acting on the system taken about any point.

(b) Both torque and angular momentum are vectors.

The time rate of angular momentum of a system of particles about a point is equal to the sum of the external torques acting on the system taken about the same point. Both torque and angular momentum are vectors.

#### The angular speed and angular acceleration of the second hand of a clock is ____ and ____ respectively.

The angular speed of the seconds hand of a clock is constant and hence its angular acceleration is zero.

A seconds hand takes one minute or 60 second to make rotation.

ω=Δθ/Δt=2π/60=π/30rad/s.

#### When ____ the force acting on a rigid body will not be able to rotate it.

In both the cases (a) when the force acting on the rigid body is parallel to the axis of rotation.

#### ____ is an example of a rigid body moving with angular acceleration.

Except the fan, remaining all objects moved with constant angular velocity. Angular speed of the fan gradually increases and hence it is moving with angular acceleration.

#### The angular momentum of a rigid body is conserved when ____.

Angular momentum of a rigid body is conserved if the total external torque acting is zero.

#### For a car moving along a straight line with uniforms speed ____ is constant and for the earth rotating about its own axis ____ about the axis is constant.

When a car is moving along a straight line path with uniform speed, its linear momentum is constant. For the earth rotating about its own axis, the angular momentum is constant.

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