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.
When a pendulum is taken to the moon, its time period increases. This is because the gravitational acceleration on the moon is about one-sixth that of Earth's. As the time period of a pendulum depends on the square root of the length divided by the gravitational acceleration, with a weaker gravity oRead more
When a pendulum is taken to the moon, its time period increases. This is because the gravitational acceleration on the moon is about one-sixth that of Earth’s. As the time period of a pendulum depends on the square root of the length divided by the gravitational acceleration, with a weaker gravity on the moon, the time period becomes longer. Therefore, the pendulum swings slower, taking more time to complete each cycle. As a result, the correct answer is option [D]: Will increase. This change occurs due to the altered gravitational conditions on the moon compared to Earth, highlighting the influence of gravity on the oscillation of pendulums.
The kinetic energy (K) of a particle is determined by its momentum (p) and mass (m) according to the formula K = p²/2m; option [D]. This equation illustrates that the kinetic energy is proportional to the square of the momentum and inversely proportional to twice the mass. Therefore, option [D]: p²/Read more
The kinetic energy (K) of a particle is determined by its momentum (p) and mass (m) according to the formula K = p²/2m; option [D]. This equation illustrates that the kinetic energy is proportional to the square of the momentum and inversely proportional to twice the mass. Therefore, option [D]: p²/2m, correctly reflects this relationship. The term ‘p²’ represents the square of the momentum, while ‘2m’ is twice the mass of the particle. Dividing the square of the momentum by twice the mass yields the kinetic energy of the particle. This formula is fundamental in understanding the energy associated with the motion of particles and is widely used in various fields of physics, including mechanics and quantum mechanics, to analyze the behavior of particles in motion.
Why 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 lessWhen the pendulum is taken to the moon, its time period
When a pendulum is taken to the moon, its time period increases. This is because the gravitational acceleration on the moon is about one-sixth that of Earth's. As the time period of a pendulum depends on the square root of the length divided by the gravitational acceleration, with a weaker gravity oRead more
When a pendulum is taken to the moon, its time period increases. This is because the gravitational acceleration on the moon is about one-sixth that of Earth’s. As the time period of a pendulum depends on the square root of the length divided by the gravitational acceleration, with a weaker gravity on the moon, the time period becomes longer. Therefore, the pendulum swings slower, taking more time to complete each cycle. As a result, the correct answer is option [D]: Will increase. This change occurs due to the altered gravitational conditions on the moon compared to Earth, highlighting the influence of gravity on the oscillation of pendulums.
See lessThe mass of a particle is m and momentum is p. Its kinetic energy will be
The kinetic energy (K) of a particle is determined by its momentum (p) and mass (m) according to the formula K = p²/2m; option [D]. This equation illustrates that the kinetic energy is proportional to the square of the momentum and inversely proportional to twice the mass. Therefore, option [D]: p²/Read more
The kinetic energy (K) of a particle is determined by its momentum (p) and mass (m) according to the formula K = p²/2m; option [D]. This equation illustrates that the kinetic energy is proportional to the square of the momentum and inversely proportional to twice the mass. Therefore, option [D]: p²/2m, correctly reflects this relationship. The term ‘p²’ represents the square of the momentum, while ‘2m’ is twice the mass of the particle. Dividing the square of the momentum by twice the mass yields the kinetic energy of the particle. This formula is fundamental in understanding the energy associated with the motion of particles and is widely used in various fields of physics, including mechanics and quantum mechanics, to analyze the behavior of particles in motion.
See less