System of Particles & Rotational Motion Test

Result

System of Particles & Rotational Motion Test - 10

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Question 1
1 / -0

Two discs of moments of inertia I₁ and I₂ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds I₁ and I₂ are brought into contact face to face with their axes of rotation coincident. What is the angular speed of the two disc system?

A

B

C

D

Solution

As there is no any external force acting between the two discs so according to law of conservation of angular momentum, we get
L= Iω
So, I1ω1 + I2ω2 = (I1 + I2) ω
Question 2
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Which of the following doesn’t use the application of Conservation of Angular Momentum?

A
Cat landing gently on feet

B
A skater performing a fast spin

C
A diver performing somersaults while diving

D
Fruit falling off the tree

Solution

Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum. All the top 3 options use the application conversion of angular momentum.
But the cause of fruit drop can occur due to many reasons such as a severe pest infestation can stress the tree enough to cause fruit drop, Sudden changes in temperature, particularly when high temperatures occur at or shortly after fruit set, can cause fruit drop.
Question 3
1 / -0

Space craft orientation is based on the principle of:

A
conservation of energy

B
conservation of linear momentum

C
conservation of angular momentum

D
all of the above

Solution

Conservation of angular momentum is a physical property of a spinning system such that its spin remains constant unless it is acted upon by an external torque; put another way, the speed of rotation is constant as long as net torque is zero.
Question 4
1 / -0

What is the relation between torque and angular momentum?

A
T = ωl

B

C
T = L/t

D
T = lω²
Question 5
1 / -0

A circus acrobat while performing spins brings his limbs closer to the body. Due to this

A
Moment of inertia increases and angular velocity increases

B
Moment of inertia decreases and angular velocity decreases

C
Moment of inertia increases and angular velocity decreases

D
Moment of inertia decreases and angular velocity increases

Solution

While in the pike position the body decreases in radius as each segment moves closer to the axis of rotation, resulting in angular velocity increasing and a decrease of moment of inertia. Thus, during a dive, angular momentum is constant meaning that moment of inertia is inversely proportional to angular velocity.
Question 6
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An earth satellite is moving around the earth in a circular orbit. In such case, what is conserved?

A
angular momentum

B
force

C
linear momentum

D
velocity

Solution

Angular Momentum is conserved
Mvr = constant
We can say that v is proportional to 1/r. When satellite stays near earth then velocity of the satellite is maximum.
Question 7
1 / -0

A child can balance himself on a moving cycle than on a stationary cycle. Based on

A
Conservation of Angular Momentum

B
Conservation of Energy

C
Conservation of Momentum

D
Conservation of Kinetic Energy Only

Solution

Spinning wheels have angular momentum, and when you're sitting on a bike, you and it and its wheels make up a system that obeys the principle of conservation of angular momentum.
Question 8
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A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rpm. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment if inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.

A
16 rpm

B
100 rpm

C
40 rpm

D
Given data is not sufficient.

Solution

Angular momentum is conserved.
I1w1 = I2w2
I2 = (2/5)I1
I1(40) = (2/5)I1w2
w2 = 100 rpm
Question 9
1 / -0

A circus acrobat while performing spins brings his limbs closer to the body. Due to this

A
Angular Momentum is conserved but K.E. is not conserved

B
Angular Momentum is not conserved and also K.E. is not conserved.

C
Angular Momentum is not conserved but K.E. is conserved

D
Angular Momentum is conserved and also K.E. is conserved

Solution

Because when the moment of inertia decreases, rotational kinetic energy increases as work is done in decreasing the moment of inertia of the body.
A circus acrobat performs feats involving spin by bringing his arms and legs closer to his body or vice versa. On bringing the arms and legs closer to the body, his moment of inertia decreases. Hence his angular velocity increases. The reverse is also true.
Question 10
1 / -0

In system international, angular momentum is measured in

A
J

B
J s^-1

C
W

D
J s

Solution

L=Iω²(L- angular momentum)
I(moment of inertia)=mr²
L=1×1×100/60
L=1.6 kgm²s^-1
≈1.9 kgm²s^-1