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.
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.
The reason for the curdling of milk is Lactobacillus. This bacterium is a type of lactic acid bacteria that plays a key role in the fermentation of milk. When added to milk, Lactobacillus converts lactose, the natural sugar in milk, into lactic acid. The increase in lactic acid causes the pH of theRead more
The reason for the curdling of milk is Lactobacillus. This bacterium is a type of lactic acid bacteria that plays a key role in the fermentation of milk. When added to milk, Lactobacillus converts lactose, the natural sugar in milk, into lactic acid. The increase in lactic acid causes the pH of the milk to decrease, leading to the coagulation of proteins such as casein. This process results in the formation of curds, which are used to make curd, yogurt, and other dairy products. The action of Lactobacillus not only curdles the milk but also imparts a tangy flavor and enhances the nutritional value of the final product. The other options, Mycobacterium, Staphylococcus, and Yeast, do not contribute significantly to the curdling of milk in the context of making curd.
Rhizobium is a symbiotic nitrogen-fixing bacterium. It forms a mutualistic relationship with leguminous plants such as peas, beans, and clover. Rhizobium resides in the root nodules of these plants and converts atmospheric nitrogen into ammonia, a form of nitrogen that plants can use for growth. ThiRead more
Rhizobium is a symbiotic nitrogen-fixing bacterium. It forms a mutualistic relationship with leguminous plants such as peas, beans, and clover. Rhizobium resides in the root nodules of these plants and converts atmospheric nitrogen into ammonia, a form of nitrogen that plants can use for growth. This process is known as biological nitrogen fixation and is crucial for soil fertility and the productivity of crops. The relationship between Rhizobium and leguminous plants is beneficial for both parties: the bacterium gets carbohydrates from the plant, while the plant receives a natural source of nitrogen. This natural fertilization process is important for sustainable agriculture and reducing the need for chemical fertilizers.
The first discovery of a virus is credited to Dmitri Ivanovsky, a Russian biologist. In 1892, Ivanovsky was investigating a disease affecting tobacco plants known as tobacco mosaic disease. He found that the infectious agent causing the disease could pass through filters that trapped bacteria. ThisRead more
The first discovery of a virus is credited to Dmitri Ivanovsky, a Russian biologist. In 1892, Ivanovsky was investigating a disease affecting tobacco plants known as tobacco mosaic disease. He found that the infectious agent causing the disease could pass through filters that trapped bacteria. This observation led him to conclude that the infectious agent was smaller than bacteria and could not be seen under a light microscope. His work laid the foundation for the concept of a virus, which was later expanded upon by other scientists. While Ivanovsky did not use the term “virus,” his discovery was a significant milestone in the field of microbiology and virology, paving the way for future research into viral diseases and their impact on plants, animals, and humans.
Time 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 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 lessThe reason for curdling of milk is
The reason for the curdling of milk is Lactobacillus. This bacterium is a type of lactic acid bacteria that plays a key role in the fermentation of milk. When added to milk, Lactobacillus converts lactose, the natural sugar in milk, into lactic acid. The increase in lactic acid causes the pH of theRead more
The reason for the curdling of milk is Lactobacillus. This bacterium is a type of lactic acid bacteria that plays a key role in the fermentation of milk. When added to milk, Lactobacillus converts lactose, the natural sugar in milk, into lactic acid. The increase in lactic acid causes the pH of the milk to decrease, leading to the coagulation of proteins such as casein. This process results in the formation of curds, which are used to make curd, yogurt, and other dairy products. The action of Lactobacillus not only curdles the milk but also imparts a tangy flavor and enhances the nutritional value of the final product. The other options, Mycobacterium, Staphylococcus, and Yeast, do not contribute significantly to the curdling of milk in the context of making curd.
See lessWhich of the following is a symbiotic nitrogen fixing bacterium?
Rhizobium is a symbiotic nitrogen-fixing bacterium. It forms a mutualistic relationship with leguminous plants such as peas, beans, and clover. Rhizobium resides in the root nodules of these plants and converts atmospheric nitrogen into ammonia, a form of nitrogen that plants can use for growth. ThiRead more
Rhizobium is a symbiotic nitrogen-fixing bacterium. It forms a mutualistic relationship with leguminous plants such as peas, beans, and clover. Rhizobium resides in the root nodules of these plants and converts atmospheric nitrogen into ammonia, a form of nitrogen that plants can use for growth. This process is known as biological nitrogen fixation and is crucial for soil fertility and the productivity of crops. The relationship between Rhizobium and leguminous plants is beneficial for both parties: the bacterium gets carbohydrates from the plant, while the plant receives a natural source of nitrogen. This natural fertilization process is important for sustainable agriculture and reducing the need for chemical fertilizers.
See lessWho discovered the virus first?
The first discovery of a virus is credited to Dmitri Ivanovsky, a Russian biologist. In 1892, Ivanovsky was investigating a disease affecting tobacco plants known as tobacco mosaic disease. He found that the infectious agent causing the disease could pass through filters that trapped bacteria. ThisRead more
The first discovery of a virus is credited to Dmitri Ivanovsky, a Russian biologist. In 1892, Ivanovsky was investigating a disease affecting tobacco plants known as tobacco mosaic disease. He found that the infectious agent causing the disease could pass through filters that trapped bacteria. This observation led him to conclude that the infectious agent was smaller than bacteria and could not be seen under a light microscope. His work laid the foundation for the concept of a virus, which was later expanded upon by other scientists. While Ivanovsky did not use the term “virus,” his discovery was a significant milestone in the field of microbiology and virology, paving the way for future research into viral diseases and their impact on plants, animals, and humans.
See less