JEE Main · Physics ↓ Falling

Work, Energy and Power appeared 31 times across 3 years — 3.6% of Physics. This question is from Work Done by a Variable Force.

Year 2026 2025 2024 Total
Questions 8 15 8 31
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A force F=α+β x² acts on an object in the x-direction. The work done by the force is 5J when the object is displaced by 1 m. If the constant α=1N then β will be

Solution & Explanation

Related Formula

The work done W by a variable force component F(x) over a displacement step is given by:

W = ∫_x₁^x₂ F(x) dx
Core Logic

Assuming the object moves from the origin x=0 to x=1 m :

W = ∫₀¹ (α + β x²) dx = 5 J
Step 1: Integration and Variable Isolation

Perform the integration step :

W = [ α x + β x³3 ]₀¹ = α + (β)/(3) = 5

Given α = 1 N , substitute this into the equation to find β :

1 + (β)/(3) = 5 (β)/(3) = 4 β = 12 N/m²
Pattern Recognition

For polynomial forces, the integration steps always yield fractional coefficients matching their power index (1 for constant, (1)/(3) for squared terms).

Chapter Mix

Class 11 Physics: Work, Energy and Power

More Work, Energy and Power Previous-Year Questions — Page 7

Q49 jee_main_2024_31_jan_morning Conservation Of Momentum
An artillery piece of mass M₁ fires a shell of mass M₂ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :
  • A. M₁ / (M₁ + M₂)
  • B. (M₂)/(M₁)
  • C. M₂ / (M₁ + M₂)
  • D. (M₁)/(M₂)

Solution

Related Formula
KE = (p²)/(2m)
Core Logic

By conservation of linear momentum (since no external horizontal force acts on the system):

0 = M₁ v₁ + M₂ v₂ | p₁| = | p₂| = p

Both the artillery and the shell acquire the exact same magnitude of momentum during firing.

Step 2: Kinetic Energy Ratio

The kinetic energy is related to momentum by KE = (p²)/(2m). Since p is identical for both bodies:

KE ∝ (1)/(m)

Therefore, the ratio of kinetic energy of the artillery (M₁) to the shell (M₂) is:

KE₁KE₂ = ((p²)/(2M₁))/((p²)/(2M₂)) = (M₂)/(M₁)
Chapter Mix

Class 11 Physics: Work, Energy And Power

More Work, Energy and Power Questions — jee_main_2025_24_jan_morning

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Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)