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A simple pendulum bob has a mass "m" and length "L". The bob is drawn aside such that the string is horizontal and then it is released. The velocity of the bob while it crosses the equilibrium position is
- a)√gL
- b)√2gL
- c)√5gL
- d)√3gL
Correct answer is option 'B'. Can you explain this answer?
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A simple pendulum bob has a mass "m" and length "L". The bob is drawn...
Understanding the Simple Pendulum
A simple pendulum consists of a mass (bob) attached to a string of length L. When the bob is pulled to a horizontal position and released, it swings down under the influence of gravity.
Energy Conservation Principle
- The total mechanical energy in the system is conserved.
- At the highest point (when the bob is horizontal), all energy is potential energy (PE).
- At the lowest point (equilibrium position), all energy is converted to kinetic energy (KE).
Potential Energy Calculation
- At the horizontal position, the height (h) of the bob above the equilibrium position is equal to the length of the pendulum, L.
- The potential energy (PE) at this point is given by:
PE = m * g * h = m * g * L
Kinetic Energy Calculation
- At the equilibrium position, the potential energy has converted to kinetic energy.
- The kinetic energy (KE) at this point is given by:
KE = (1/2) * m * v^2
Setting Up the Equation
- By conservation of energy:
PE_initial = KE_final
m * g * L = (1/2) * m * v^2
- Canceling mass (m) from both sides:
g * L = (1/2) * v^2
Solving for Velocity
- Rearranging the equation gives:
v^2 = 2 * g * L
v = √(2 * g * L)
Conclusion
Thus, the velocity of the pendulum bob as it crosses the equilibrium position is v = √(2gL), confirming that the correct answer is option 'B'.
A simple pendulum consists of a mass (bob) attached to a string of length L. When the bob is pulled to a horizontal position and released, it swings down under the influence of gravity.
Energy Conservation Principle
- The total mechanical energy in the system is conserved.
- At the highest point (when the bob is horizontal), all energy is potential energy (PE).
- At the lowest point (equilibrium position), all energy is converted to kinetic energy (KE).
Potential Energy Calculation
- At the horizontal position, the height (h) of the bob above the equilibrium position is equal to the length of the pendulum, L.
- The potential energy (PE) at this point is given by:
PE = m * g * h = m * g * L
Kinetic Energy Calculation
- At the equilibrium position, the potential energy has converted to kinetic energy.
- The kinetic energy (KE) at this point is given by:
KE = (1/2) * m * v^2
Setting Up the Equation
- By conservation of energy:
PE_initial = KE_final
m * g * L = (1/2) * m * v^2
- Canceling mass (m) from both sides:
g * L = (1/2) * v^2
Solving for Velocity
- Rearranging the equation gives:
v^2 = 2 * g * L
v = √(2 * g * L)
Conclusion
Thus, the velocity of the pendulum bob as it crosses the equilibrium position is v = √(2gL), confirming that the correct answer is option 'B'.
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Community Answer
A simple pendulum bob has a mass "m" and length "L". The bob is drawn...
mgL = 1/2mv2
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A simple pendulum bob has a mass "m" and length "L". The bob is drawn aside such that the string is horizontal and then it is released. The velocity of the bob while it crosses the equilibrium position isa)√gLb)√2gLc)√5gLd)√3gLCorrect answer is option 'B'. Can you explain this answer?
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