Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R). Read the statements and choose the correct answer using the code given below. Assertion (A): The layout position of gymnast makes it more difficult to somersault. Reason (R): An extended gymnast has a greater moment of inertia than a piked gymnast.
Understanding Gymnastics and Rotation
This question asks us to evaluate two statements about a gymnast's somersault and how their body position affects the rotation. We need to analyze the concepts of body layout, moment of inertia, and how they relate to the difficulty of performing a somersault.
Analyzing Assertion (A): The layout position of gymnast makes it more difficult to somersault.
The Assertion states that a layout position makes it more difficult for a gymnast to perform a somersault. A layout position means the gymnast's body is extended straight. When a gymnast somersaults, they rotate around a central axis. The difficulty of rotating, especially quickly, is related to how the mass is distributed around the axis of rotation.
In gymnastics, athletes often change their body shape during rotations (like somersaults or twists). They might start extended (layout), then pull into a tucked or piked position, and then extend again for landing. Tucking or piking involves bringing the body parts closer to the axis of rotation.
Based on physics principles related to rotation, keeping the body extended (layout) means the mass is distributed further away from the axis of rotation compared to a tucked or piked position. This distribution affects the moment of inertia, which in turn affects the ability to rotate quickly. Generally, a straight or layout position makes it harder to achieve a high angular velocity (speed of rotation) compared to a tucked or piked position, making the somersault feel more difficult or requiring more initial force to rotate.
Therefore, Assertion (A) stating that the layout position makes it more difficult to somersault appears to be true from a physics perspective.
Analyzing Reason (R): An extended gymnast has a greater moment of inertia than a piked gymnast.
The Reason discusses the concept of moment of inertia. Moment of inertia ($I$) is a measure of an object's resistance to changes in its rotational motion. It depends on the total mass and how that mass is distributed relative to the axis of rotation. The formula for moment of inertia is generally given by:
\(I = \sum m_i r_i^2\)
where \(m_i\) is the mass of each particle and \(r_i\) is its perpendicular distance from the axis of rotation. For continuous bodies, it involves integration.
When a gymnast is extended (like in a layout position), their limbs and body are stretched out. This means a significant portion of their mass is relatively far from the axis of rotation passing through the center of their body. When a gymnast is piked or tucked, they curl up, bringing their limbs and torso closer to the axis of rotation.
According to the formula for moment of inertia, if the mass is distributed further from the axis of rotation (larger \(r_i\)), the moment of inertia is greater. If the mass is distributed closer to the axis (smaller \(r_i\)), the moment of inertia is smaller.
Comparing an extended (layout) gymnast and a piked gymnast, the extended gymnast has mass further from the axis of rotation. Therefore, an extended gymnast has a greater moment of inertia than a piked gymnast. Reason (R) is true.
Connecting the Assertion and the Reason
Now we need to see if Reason (R) explains Assertion (A). The difficulty in somersaulting is related to how easily the gymnast can rotate, specifically, how quickly they can achieve angular velocity (\(\omega\)). This is governed by the conservation of angular momentum (\(L\)). Angular momentum is given by:
\(L = I\omega\)
In the absence of external torques (like air resistance, which we often ignore in simplified physics analysis), angular momentum is conserved. This means \(L\) is constant. So, if the moment of inertia (\(I\)) changes, the angular velocity (\(\omega\)) must also change to keep \(L\) constant.
- If \(I\) increases (like going from a tuck to a layout), \(\omega\) must decrease.
- If \(I\) decreases (like going from a layout to a tuck), \(\omega\) must increase.
Reason (R) states that an extended (layout) gymnast has a greater moment of inertia (\(I\)). If \(I\) is greater, then for a given angular momentum \(L\), the angular velocity \(\omega\) (\(\omega = L/I\)) will be smaller. A smaller angular velocity means the gymnast rotates more slowly.
Performing a somersault requires achieving a certain amount of rotation, often within a limited time (like before landing). If the angular velocity is smaller in a layout position due to the greater moment of inertia, it is indeed more difficult to complete the somersault, or multiple somersaults, compared to rotating in a piked or tucked position. Therefore, the greater moment of inertia in the layout position (R) directly explains why it is more difficult to somersault in that position (A).
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).
Summary Analysis
| Statement | Truth Value | Explanation |
|---|---|---|
| Assertion (A): The layout position of gymnast makes it more difficult to somersault. | True | An extended (layout) body has a higher moment of inertia, leading to slower rotation for a given angular momentum. |
| Reason (R): An extended gymnast has a greater moment of inertia than a piked gymnast. | True | When extended, mass is further from the axis of rotation, increasing moment of inertia. |
| Is (R) the correct explanation for (A)? | Yes | The greater moment of inertia in the extended position directly explains why the angular velocity is lower, making the somersault more difficult. |
Revision Table: Gymnastics Rotation Concepts
| Concept | Definition/Relation | How it Applies to Gymnastics Rotation |
|---|---|---|
| Moment of Inertia (\(I\)) | Resistance to rotational motion; depends on mass and mass distribution relative to rotation axis (\(I \propto mr^2\)). | Higher \(I\) for extended body (mass far from axis); Lower \(I\) for tucked/piked body (mass close to axis). |
| Angular Velocity (\(\omega\)) | Speed of rotation (radians or degrees per second). | Higher \(\omega\) needed for faster rotations/more somersaults in air. |
| Angular Momentum (\(L\)) | Product of moment of inertia and angular velocity (\(L = I\omega\)). Conserved in absence of external torque. | Gymnast generates \(L\) upon leaving the ground. Changing body shape changes \(I\), forcing \(\omega\) to change to conserve \(L\). |
| Conservation of Angular Momentum | Total angular momentum of a system remains constant if no external torque acts on it. | If \(I\) increases, \(\omega\) decreases. If \(I\) decreases, \(\omega\) increases (\(I_1\omega_1 = I_2\omega_2\)). |
Additional Information: Gymnastics Body Positions and Rotation
Gymnasts strategically change their body shape during aerial skills like somersaults and twists to control their rotation speed. The primary body positions used for this purpose are:
- Layout: Body is extended straight. This position has the largest moment of inertia around the somersault axis. It results in the slowest angular velocity for a given angular momentum, making it harder to complete multiple rotations but is used for certain skills and for landing preparation (slowing down rotation).
- Pike: Body is bent at the hips, with legs straight. The upper body is brought closer to the legs. This position has a smaller moment of inertia than layout but larger than tuck. It allows for faster rotation than layout.
- Tuck: Knees are pulled towards the chest, and the body is curled into a ball. This position has the smallest moment of inertia around the somersault axis. It allows for the fastest angular velocity, making it ideal for completing multiple somersaults.
By transitioning between these positions, a gymnast can effectively control their rotation speed in the air. Starting a somersault often involves generating angular momentum with an initial push or jump. Once airborne, they manipulate their moment of inertia by changing their body shape to achieve the desired rotation.
Important Questions from Training and Fitness test
A cyclist moves in a velodrome of radius of 80 m. If the coefficient of friction is 0.25, then the maximum speed with which the cyclist can take a turn without leaning inwards is
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R). Read the statements and choose the correct answer using the code given below.
Assertion (A): For observation of movement in qualitative analysis, the gymnastic coaches use the temporal information from the sound of impact with the mat.
Reason (R): A systematic observational strategy helps the gymnastic coaches to ensure the tremendous perceptual demands of observing movement.
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R). Read the statements and choose the correct answer using the code given below.
Assertion (A): The effectiveness of Ballistic method is doubted in the development of flexibility.
Reason (R): The swinging movement leads to stretch reflex in the antagonist muscle thereby hindering the optimum stretch of the concerned muscle.
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R). Read the statements and choose the correct answer using the code given below.
Assertion (A): Standard score facilitates comparison of athlete’s performance in two different events having separate units.
Reason (R): The standard score indicates as to how many standard deviations a score is above or below the mean.
Match the items of List I with the items of List II and choose the correct answer from the code given below.
List I
List II
(a)
Dimension of Torque
(i)
ML-1T-2
(b)
Dimension of Impulse
(ii)
ML2T-2
(c)
Dimension of Pressure
(iii)
M-1L3T-2
(d)
Dimension of Gravitational Constant
(iv)
MLT-1
