The fraction of the Earth's gravity that is closest to the Moon's gravity is 1/6, which is option [C]. The gravitational acceleration on the Moon's surface is approximately 1/6th of that on the Earth's surface. This means that objects on the Moon weigh approximately 1/6th of their weight on Earth. TRead more
The fraction of the Earth’s gravity that is closest to the Moon’s gravity is 1/6, which is option [C]. The gravitational acceleration on the Moon’s surface is approximately 1/6th of that on the Earth’s surface. This means that objects on the Moon weigh approximately 1/6th of their weight on Earth. The ratio of the Moon’s gravity to Earth’s gravity is commonly expressed as 1/6, making option C the most accurate choice among the provided options. This difference in gravitational acceleration is due to the Moon’s smaller mass compared to Earth, resulting in weaker gravitational attraction. Understanding this fraction is crucial for space exploration and celestial mechanics, as it influences the behavior of objects and spacecraft in lunar orbit and during lunar landings. Therefore, option C accurately represents the relationship between the Earth’s gravity and the Moon’s gravity, highlighting the significance of gravitational forces in astronomical phenomena.
The time period of a pendulum, defined as the time taken for one complete oscillation, depends on its length, which is option B. This relationship is described by the formula for the period of a simple pendulum: T=2π√(L/g )where T is the period, L is the length of the pendulum, and g is the acceleraRead more
The time period of a pendulum, defined as the time taken for one complete oscillation, depends on its length, which is option B. This relationship is described by the formula for the period of a simple pendulum: T=2π√(L/g )where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. The period of a pendulum is independent of its mass, as demonstrated by Galileo’s experiments. It is also unaffected by temperature variations in the absence of significant changes to the pendulum’s length or environmental conditions. However, changes in length, such as altering the position of the pendulum’s pivot or adding additional mass, can impact its period. Therefore, option [B] accurately identifies the primary factor determining the time period of a pendulum, highlighting the fundamental relationship between length and oscillation period in pendulum motion.
Pendulum clocks become slow in summer because the length of the pendulum increases due to thermal expansion, which is; option [C]. As the temperature rises, the pendulum rod expands, causing the effective length of the pendulum to increase. This longer length results in a longer period for each osciRead more
Pendulum clocks become slow in summer because the length of the pendulum increases due to thermal expansion, which is; option [C]. As the temperature rises, the pendulum rod expands, causing the effective length of the pendulum to increase. This longer length results in a longer period for each oscillation, leading to slower timekeeping compared to cooler temperatures. The effect of thermal expansion on the pendulum’s length alters the clock’s timing mechanism, causing it to lose time during warmer weather conditions. This phenomenon is a well-known factor affecting the accuracy of mechanical clocks and is accounted for in their design and calibration. Therefore, option C accurately identifies the reason for the slowdown of pendulum clocks during summer, emphasizing the influence of temperature-induced changes in the length of the pendulum on timekeeping precision.
If the length of a simple pendulum is increased by 4%, then its time period will increase by approximately 2%, which is; option [B]. The time period (T) of a pendulum is directly proportional to the square root of its length (L) as given by the formula, T=2π√(L/g ) where g is the acceleration due toRead more
If the length of a simple pendulum is increased by 4%, then its time period will increase by approximately 2%, which is; option [B]. The time period (T) of a pendulum is directly proportional to the square root of its length (L) as given by the formula, T=2π√(L/g ) where g is the acceleration due to gravity. When the length increases by 4%, the time period increases by approximately 2%. Therefore, option B accurately describes the change in time period resulting from a 4% increase in the length of a simple pendulum, highlighting the proportional relationship between the length and the square root of the time period in pendulum motion.
When the length of a pendulum is quadrupled, its time of swing increases proportionally. The relationship between the length of a pendulum (L) and its time period (T) is described by the formula T = 2π√(L/g), where g is the acceleration due to gravity. If the length (L) is quadrupled, it means L becRead more
When the length of a pendulum is quadrupled, its time of swing increases proportionally. The relationship between the length of a pendulum (L) and its time period (T) is described by the formula T = 2π√(L/g), where g is the acceleration due to gravity. If the length (L) is quadrupled, it means L becomes 4L. Substituting 4L into the formula gives T = 2π√(4L/g), which simplifies to T = 2π√(4/g)√L. √(4/g) is a constant, so it comes out of the square root, yielding T = 2π(2/√g)√L. Thus, the time period becomes four times the original value. Therefore, the correct answer is option [D]: becomes four times. This illustrates the direct relationship between the length of a pendulum and its time period.
What fraction of the Earth’s gravity is closest to the Moon’s gravity?
The fraction of the Earth's gravity that is closest to the Moon's gravity is 1/6, which is option [C]. The gravitational acceleration on the Moon's surface is approximately 1/6th of that on the Earth's surface. This means that objects on the Moon weigh approximately 1/6th of their weight on Earth. TRead more
The fraction of the Earth’s gravity that is closest to the Moon’s gravity is 1/6, which is option [C]. The gravitational acceleration on the Moon’s surface is approximately 1/6th of that on the Earth’s surface. This means that objects on the Moon weigh approximately 1/6th of their weight on Earth. The ratio of the Moon’s gravity to Earth’s gravity is commonly expressed as 1/6, making option C the most accurate choice among the provided options. This difference in gravitational acceleration is due to the Moon’s smaller mass compared to Earth, resulting in weaker gravitational attraction. Understanding this fraction is crucial for space exploration and celestial mechanics, as it influences the behavior of objects and spacecraft in lunar orbit and during lunar landings. Therefore, option C accurately represents the relationship between the Earth’s gravity and the Moon’s gravity, highlighting the significance of gravitational forces in astronomical phenomena.
See lessTime Period of the pendulum
The time period of a pendulum, defined as the time taken for one complete oscillation, depends on its length, which is option B. This relationship is described by the formula for the period of a simple pendulum: T=2π√(L/g )where T is the period, L is the length of the pendulum, and g is the acceleraRead more
The time period of a pendulum, defined as the time taken for one complete oscillation, depends on its length, which is option B. This relationship is described by the formula for the period of a simple pendulum: T=2π√(L/g )where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. The period of a pendulum is independent of its mass, as demonstrated by Galileo’s experiments. It is also unaffected by temperature variations in the absence of significant changes to the pendulum’s length or environmental conditions. However, changes in length, such as altering the position of the pendulum’s pivot or adding additional mass, can impact its period. Therefore, option [B] accurately identifies the primary factor determining the time period of a pendulum, highlighting the fundamental relationship between length and oscillation period in pendulum motion.
See lessWhy do pendulum clocks become slow in summer?
Pendulum clocks become slow in summer because the length of the pendulum increases due to thermal expansion, which is; option [C]. As the temperature rises, the pendulum rod expands, causing the effective length of the pendulum to increase. This longer length results in a longer period for each osciRead more
Pendulum clocks become slow in summer because the length of the pendulum increases due to thermal expansion, which is; option [C]. As the temperature rises, the pendulum rod expands, causing the effective length of the pendulum to increase. This longer length results in a longer period for each oscillation, leading to slower timekeeping compared to cooler temperatures. The effect of thermal expansion on the pendulum’s length alters the clock’s timing mechanism, causing it to lose time during warmer weather conditions. This phenomenon is a well-known factor affecting the accuracy of mechanical clocks and is accounted for in their design and calibration. Therefore, option C accurately identifies the reason for the slowdown of pendulum clocks during summer, emphasizing the influence of temperature-induced changes in the length of the pendulum on timekeeping precision.
See lessIf the length of a simple pendulum is increased by 4%, then its time period will
If the length of a simple pendulum is increased by 4%, then its time period will increase by approximately 2%, which is; option [B]. The time period (T) of a pendulum is directly proportional to the square root of its length (L) as given by the formula, T=2π√(L/g ) where g is the acceleration due toRead more
If the length of a simple pendulum is increased by 4%, then its time period will increase by approximately 2%, which is; option [B]. The time period (T) of a pendulum is directly proportional to the square root of its length (L) as given by the formula, T=2π√(L/g ) where g is the acceleration due to gravity. When the length increases by 4%, the time period increases by approximately 2%. Therefore, option B accurately describes the change in time period resulting from a 4% increase in the length of a simple pendulum, highlighting the proportional relationship between the length and the square root of the time period in pendulum motion.
See lessIf the length of the pendulum is quadrupled, then the time of swing of the pendulum is
When the length of a pendulum is quadrupled, its time of swing increases proportionally. The relationship between the length of a pendulum (L) and its time period (T) is described by the formula T = 2π√(L/g), where g is the acceleration due to gravity. If the length (L) is quadrupled, it means L becRead more
When the length of a pendulum is quadrupled, its time of swing increases proportionally. The relationship between the length of a pendulum (L) and its time period (T) is described by the formula T = 2π√(L/g), where g is the acceleration due to gravity. If the length (L) is quadrupled, it means L becomes 4L. Substituting 4L into the formula gives T = 2π√(4L/g), which simplifies to T = 2π√(4/g)√L. √(4/g) is a constant, so it comes out of the square root, yielding T = 2π(2/√g)√L. Thus, the time period becomes four times the original value. Therefore, the correct answer is option [D]: becomes four times. This illustrates the direct relationship between the length of a pendulum and its time period.
See less