Potential Energy : Numerical Problems
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2) Potential Energy
Q1. An object of mass 10 kg is lifted to a height of 5 m. Calculate the potential energy gained.
āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§§ā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Ģ āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻāĻ ā§ā§ąāĻž āĻš’āĻ˛āĨ¤ āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 10 kg , Height (h) = 5 m , g = 9.8 m/s²
Formula / āĻ¸ā§āĻ¤ā§ā§°: Potential Energy (PE) = mgh (āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh)
Calculation / āĻāĻŖāĻ¨āĻž: PE = 10 × 9.8 × 5 = 490 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Potential Energy gained = 490 Joules (āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = ā§Ēā§¯ā§Ļ āĻā§āĻ˛)
Q2. An object of mass 5 kg is lifted vertically through a height of 8 m. Calculate the potential energy gained.
āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§Ģ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ āĻā§°ā§āĻĻā§āĻ§ āĻĻāĻŋāĻļā§ ā§Ž āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻāĻ ā§ā§ąāĻž āĻš’āĻ˛āĨ¤ āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 5 kg , Height (h) = 8 m , g = 9.8 m/s²
Formula / āĻ¸ā§āĻ¤ā§ā§°: Potential Energy (PE) = mgh (āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh)
Calculation / āĻāĻŖāĻ¨āĻž: PE = 5 × 9.8 × 8 = 392 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Potential Energy gained = 392 Joules (āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = ā§Šā§¯ā§¨ āĻā§āĻ˛)
Q3. A book of mass 2 kg is lifted to a shelf 3 m high. Calculate the potential energy gained by the book.
āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻŋāĻ¤āĻžāĻĒā§° āĻā§° ā§¨ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Š āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžā§° āĻļā§āĻ˛ā§āĻĢāĻ¤ āĻ¤ā§āĻ˛āĻž āĻš’āĻ˛āĨ¤ āĻāĻŋāĻ¤āĻžāĻĒāĻāĻ¨ā§ āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨ ?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 2 kg , Height (h) = 3 m , g = 9.8 m/s²
Formula / āĻ¸ā§āĻ¤ā§ā§°: Potential Energy (PE) = mgh (āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh)
Calculation / āĻāĻŖāĻ¨āĻž: PE = 2 × 9.8 × 3 = 58.8 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Potential Energy gained = 58.8 Joules (āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = ā§Ģā§Ž.ā§Ž āĻā§āĻ˛)
Q4. An object of mass 7 kg is lifted to a height of 6 m. Calculate the potential energy gained.
āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Ŧ āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻāĻ ā§ā§ąāĻž āĻš’āĻ˛āĨ¤ āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 7 kg , Height (h) = 6 m , g = 9.8 m/s²
Formula / āĻ¸ā§āĻ¤ā§ā§°: Potential Energy (PE) = mgh (āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh)
Calculation / āĻāĻŖāĻ¨āĻž: PE = 7 × 9.8 × 6 = 411.6 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Potential Energy gained = 411.6 Joules (āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = ā§Ēā§§ā§§.ā§Ŧ āĻā§āĻ˛)
Q5. An object of mass 8 kg is lifted to a height of 4 m. Calculate the potential energy gained. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§Ž āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Ē āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻāĻ ā§ā§ąāĻž āĻš’āĻ˛āĨ¤ āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 8 kg , Height (h) = 4 m , g = 9.8 m/s²
Formula / āĻ¸ā§āĻ¤ā§ā§°: Potential Energy (PE) = mgh (āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh)
Calculation / āĻāĻŖāĻ¨āĻž: PE = 8 × 9.8 × 4 = 313.6 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Potential Energy gained = 313.6 Joules (āĻ˛āĻžāĻ āĻā§°āĻž āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = ā§Šā§§ā§Š.ā§Ŧ āĻā§āĻ˛)
Q6. An object of mass 5 kg is lifted to a height of 10 m. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§Ģ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§§ā§Ļ āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻāĻ ā§ā§ąāĻž āĻš’āĻ˛āĨ¤
Formula: PE = mgh (āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh
Calculation: PE = 5 × 9.8 × 10 = 490 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 490 Joules / ā§Ēā§¯ā§Ļ āĻā§āĻ˛
Q7. A book of mass 2 kg is kept on a shelf 4 m high. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻŋāĻ¤āĻžāĻĒā§° āĻā§° ā§¨ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Ē āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžā§° āĻļā§āĻ˛ā§āĻĢāĻ¤ ā§°āĻžāĻāĻŋāĻ˛ā§āĨ¤
Calculation: PE = 2 × 9.8 × 4 = 78.4 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 78.4 Joules / ā§ā§Ž.ā§Ē āĻā§āĻ˛
Q8. A body of mass 10 kg is lifted to 3 m. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§§ā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Š āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻ¤ā§āĻ˛āĻŋāĻ˛ā§āĨ¤
Calculation: PE = 10 × 9.8 × 3 = 294 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 294 Joules / ā§¨ā§¯ā§Ē āĻā§āĻ˛
Q9. An object of mass 6 kg is raised to 5 m. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§Ŧ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§Ģ āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻ¤ā§āĻ˛āĻŋāĻ˛ā§āĨ¤
Calculation: PE = 6 × 9.8 × 5 = 294 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 294 Joules / ā§¨ā§¯ā§Ē āĻā§āĻ˛
Q10. A load of mass 15 kg is lifted through 2 m. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦā§āĻāĻžā§° āĻā§° ā§§ā§Ģ āĻā§āĻāĻŋ āĻā§°ā§ āĻ¤āĻžāĻ ā§¨ āĻŽāĻŋāĻāĻžā§° āĻāĻā§āĻāĻ¤āĻžāĻ˛ā§ āĻ¤ā§āĻ˛āĻŋāĻ˛ā§āĨ¤
Calculation: PE = 15 × 9.8 × 2 = 294 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 294 Joules / ā§¨ā§¯ā§Ē āĻā§āĻ˛
Exam Tips :
- Always write: Given → Formula → Calculation → Answer
- Don’t forget units (J, N, m, kg)
- Steps clearly āĻĻā§āĻā§ā§ąāĻžāĻ˛ā§ full marks āĻĒā§ā§ąāĻž āĻ¯āĻžāĻ¯āĻŧ
- Always write Given, Formula, Calculation, Answer