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.
Hooke's principle is related to elasticity; option [B]. It states that the force required to extend or compress an elastic material, like a spring, is directly proportional to the displacement or deformation of that material. This principle applies to various materials, not just springs, and is fundRead more
Hooke’s principle is related to elasticity; option [B]. It states that the force required to extend or compress an elastic material, like a spring, is directly proportional to the displacement or deformation of that material. This principle applies to various materials, not just springs, and is fundamental in understanding their behavior under stress. It’s extensively used in fields such as mechanical engineering, materials science, and structural analysis to predict and design the response of structures and components to applied loads. Hooke’s principle enables engineers and scientists to calculate stresses and strains, determine material properties, and design resilient structures. Therefore, option [B]: By elasticity, correctly reflects the association between Hooke’s principle and the behavior of elastic materials, emphasizing its significance in understanding the mechanical properties of solids undergoing deformation.
If 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 lessHooke’s principle is related to which of the following?
Hooke's principle is related to elasticity; option [B]. It states that the force required to extend or compress an elastic material, like a spring, is directly proportional to the displacement or deformation of that material. This principle applies to various materials, not just springs, and is fundRead more
Hooke’s principle is related to elasticity; option [B]. It states that the force required to extend or compress an elastic material, like a spring, is directly proportional to the displacement or deformation of that material. This principle applies to various materials, not just springs, and is fundamental in understanding their behavior under stress. It’s extensively used in fields such as mechanical engineering, materials science, and structural analysis to predict and design the response of structures and components to applied loads. Hooke’s principle enables engineers and scientists to calculate stresses and strains, determine material properties, and design resilient structures. Therefore, option [B]: By elasticity, correctly reflects the association between Hooke’s principle and the behavior of elastic materials, emphasizing its significance in understanding the mechanical properties of solids undergoing deformation.
See less