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A wire whose cross-sectional area is 2 mm² is stretched by 0.1 mm by a certain load, and if a similar wire of triple the area of cross-section is stretched by the same load, then the elongation of the second wire would be
The formula for the elongation of a wire is as follows: ΔL = (F L) / (A Y) Where: ΔL is the elongation, F is the force, L is the original length of the wire, A is the cross-sectional area, Y is Young's Modulus. For the first wire, the elongation is given by: ΔL1 = (F L) / (A1 Y) For the second wire,Read more
The formula for the elongation of a wire is as follows:
ΔL = (F L) / (A Y)
Where:
ΔL is the elongation,
F is the force,
L is the original length of the wire,
A is the cross-sectional area,
Y is Young’s Modulus.
For the first wire, the elongation is given by:
ΔL1 = (F L) / (A1 Y)
For the second wire, the elongation is given by:
ΔL2 = (F L) / (A2 Y)
Since the area of the second wire is three times that of the first wire, A2 = 3 A1, we can compare the elongations:
ΔL2 / ΔL1 = A1 / A2 = 1 / 3
Thus, the elongation of the second wire is one-third that of the first wire:
ΔL2 = ΔL1 / 3 = 0.1 mm / 3 = 0.033 mm
The correct answer is:
0.033 mm
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Why should practitioners avoid forcing deep breathing during Āsanas?
Deep or forced breathing during Āsanas may create unnecessary tension, reducing the pose's effectiveness and increasing the risk of discomfort or strain. Breathing naturally through the nose supports the body's rhythm, ensures oxygen flow, and maintains relaxation. This mindful approach fosters a haRead more
Deep or forced breathing during Āsanas may create unnecessary tension, reducing the pose’s effectiveness and increasing the risk of discomfort or strain. Breathing naturally through the nose supports the body’s rhythm, ensures oxygen flow, and maintains relaxation. This mindful approach fosters a harmonious balance between movement and breath, enhancing the physical and mental benefits of the practice.
See lessA sphere of radius 3 cm is subjected to a pressure of 100 atm. Its volume decreases by 0.3 c.c. What will be its bulk modulus?
We can use the formula to find the bulk modulus as follows: Bulk Modulus (B) = (Pressure × ΔV) / V Where: - Pressure P = 100 atm - Change in volume ΔV = 0.3 c.c. - Initial volume V of the sphere is given by the formula for the volume of a sphere: V = (4/3) π r³ For r = 3 cm: V = (4/3) π (3)³ = 36 πRead more
We can use the formula to find the bulk modulus as follows:
Bulk Modulus (B) = (Pressure × ΔV) / V
Where:
– Pressure P = 100 atm
– Change in volume ΔV = 0.3 c.c.
– Initial volume V of the sphere is given by the formula for the volume of a sphere:
V = (4/3) π r³
For r = 3 cm:
V = (4/3) π (3)³ = 36 π c.c.
Now, let’s calculate the bulk modulus:
B = (100 atm × 0.3 c.c.) / (36 π c.c.)
Simplifying the above expression gives us the answer
B = 4 π × 10⁵ atm
Thus the correct answer is
4π x 10⁵ atm
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What are Rabbit breathing and Dog breathing and how do they benefit the lungs?
Rabbit breathing involves slow, rhythmic breaths, improving lung capacity and encouraging relaxation. Dog breathing mimics rapid breaths, releasing excess heat and enhancing breath awareness. Together, they strengthen respiratory muscles, increase oxygen flow, and prepare the lungs for Prānāyāma. ThRead more
Rabbit breathing involves slow, rhythmic breaths, improving lung capacity and encouraging relaxation. Dog breathing mimics rapid breaths, releasing excess heat and enhancing breath awareness. Together, they strengthen respiratory muscles, increase oxygen flow, and prepare the lungs for Prānāyāma. These exercises improve breathing efficiency, promote calmness, and ensure better lung health, essential for a balanced and effective Yoga practice.
See lessWhat are Sūkshma Vyāyāma and Śithalīkarana Vyāyāma, and why are they important?
Sūkshma Vyāyāma involves loosening joints to increase mobility, while Śithalīkarana Vyāyāma focuses on flexing the spine to enhance flexibility and posture. These preparatory exercises warm up the body, prevent injuries, and improve lung function. By ensuring physical readiness, they create a strongRead more
Sūkshma Vyāyāma involves loosening joints to increase mobility, while Śithalīkarana Vyāyāma focuses on flexing the spine to enhance flexibility and posture. These preparatory exercises warm up the body, prevent injuries, and improve lung function. By ensuring physical readiness, they create a strong foundation for advanced practices like Āsanas and Prānāyāma, promoting a safe and effective Yogic experience.
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