Some Numerical and Conceptual Question in Circular Motion

Question 1: An object of mass 8kg is whirled round in vertical circle of radius 2m with a constant speed of 6m/sec. Calculate the maximum and minimum tension in the string.

Solution:

Here, we have,

Mass of object (m)=8kg

Radius of vertical circle (r)=2m

Speed (v)=6m/sec

Then, The tension while maximum at the lowest point of the circle. At this point,

T (max) = ((mv^2)/r)+ma

=((8*6^2)/2)+8*10

=224N

Now, The tension will be minimum at the highest point of circle,

T (mini) = ((mv^2)/r)-mg

=((8*6^2)/2)-8*10

=64N

Question 2: An object of mass 10kg whirled round a horizontal circle of radius 4m by a revolving string inclined to the vertical. If the uniform speed of the object is 5m/sec. Calculate

i) Tension in the string?

ii) Angle of inclination of the string to the vertical?

Solution:

Here, we have,

Mass of object (m)=10kg

Radius of horizontal circle (r)=4m

Velocity (v)=5m/sec

we know,

tanƟ=v^2/r*g

Or, tanƟ=(5^2/4*10)

Or, tanƟ=25/40

i.e. Ɵ = 32

Again,

T CosƟ=mg

Or, T=m*g/CosƟ   

i.e. T=103N

Question 3: Find the maximum speed at which car turn a curve of 30m radius on a level road. If coefficient of friction between tires and radius is 0.4

Solution:

Here, we have,

Radius of curve (r)=30m

Coefficient of friction between tires and radius (µ) = 0.4

Maximum speed (v)=?

Now,

v=õ *rg

=√0.4 *30*10

=√120 m/sec

Question 4: Calculate the magnitude of centripetal force which keeps a body of mass 0.2kg moving in a horizontal circle of radius 0.5m with a period of 0.5sec.

Solution:

Here, we have,

Mass of body (m)=0.2kg

Radius of horizontal circle (r)=0.5m

Time taken (t)=0.5sec

Magnitude of centripetal force (Fc)=?

For horizontal motion,

Fc=((mv^2)/r)

=(m(w*r)^2)/r

=m*(2pi/t)^2*r

=m*w^2*r

=0.2kg*(4*(3.14)^2)*0.5/(0.5*0.5)

=15.8N

Question 5: A pendulum block attached to a string of length 1m will break when the in it exceed 22N .Calculate the mass of the bob which breaks the string. If it is revolving with constant speed of 10m/sec. (g=10m/sec^2)

Solution:

Here, we have,

Tension (T)=22N

Length of string (l=r)=1m

Speed (v)=10m/sec^2

Aceeleration due to gravity (g)=10m/sec^2

The string will be breaks in vertical when tension is developed 22N. It means the body is at the lowest point of the circle.

T= ((mv^2)/r)+mg

Or, 22= ((m*10^2)/1)+m*10

Or, 22 = m(100+10)

Or, 22=110m

i.e. m=0.2kg 

Question 6: What is the source of centripetal force to a satellite revolving round the earth?

Answer: 

The source of centripetal force to a satellite revolving round the earth is gravitational force between satellite and the earth. By this force, satellite revolves round the earth.

Question 7: Is it possible to have acceleration in a body even if its speed constant?

Answer: 

When a body revolves in a circle with uniform speed, it has acceleration because the direction of velocity changes and the magnitude of velocity (speed) remain constant. When a particle moving with uniform speed 'v', the magnitude of acceleration is v^2/r always remain constant by its direction towards the center of circle.

Question 8: In a circus, why does a motor cyclist not fall down when he moves on vertical wall ?

Answer:

The motorcyclist moving on a vertical wall keeps himself slightly bent and expresses two forces. The vertical component balances weight of cyclist and balances motorcyclist and his vehicle and other component acts towards the center of a circle and balance centripetal force. Also, centripetal force is equal to centrifugal force.

Question 9: Cream separates out when milk is churned,why?

Answer: 

When milk rotated in a cylinder, the particle of the milk also rotates. The particle of milk is heavier than particle of cream. The lighter particle experiences less centripetal force than heavier particle. Therefore, lighter and heavier particle do not revolve in same orbit.

The lighter cream particle flows circular path of smaller radius and collect near the center where as heavier particles of milk follows circular path of larger radius which are separated away from center (i.e. axle). In this way, cream separate from the milk.