A lens which is thicker at center and thinner at edges is MCQ with Answer and Explanation

Explanation:
Escape velocity v_e = √(2GM/R), where M is planet mass, R its radius. Thus v_e depends on both M and R. It is independent of the escaping body's mass (as gravitational and inertial mass cancel). Memory tip: 'v_e ∝ √(M/R); larger M or smaller R ⇒ higher escape velocity'. This gravitation formula application is frequently tested in competitive exams. Always recall that escape velocity is a property of the planet, not the projectile. This problem assesses understanding of gravitational potential energy concepts.

Explanation:
Proton mass ≈ 1.67 × 10⁻²⁷ kg, electron ≈ 9.11 × 10⁻³¹ kg, ratio ≈ 1836. Neutron slightly heavier. Atomic mass concentrated in nucleus.

Explanation:
Work done by a variable force is the definite integral of F dx. W = Integral(3x^2 + 2x) dx from 1 to 2. W = [x^3 + x^2] evaluated from 1 to 2. Upper limit: (2^3 + 2^2) = 8 + 4 = 12. Lower limit: (1^3 + 1^2) = 1 + 1 = 2. Work = 12 - 2 = 10 Joules.