Questions focused on potential energy within mass systems, including energy calculations and real-world applications. Ideal for physics exam preparation.
vf2 = vi2−ve2. vf2 = (11.8)2−(11.2)2 = 139.24−125.44 = 13.8. vf = 13.8≈3.71km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.7 km/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Escape speed (ve = 2GMR) is the minimum speed where kinetic energy equals the gravitational potential energy’s magnitude, ensuring total energy is zero, allowing escape to infinity. As per NCERT, applying relevant law/formula with correct units and sign convention leads to To balance kinetic and potential energy. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Outside shell: F = GMmr2. F = 6.67×10−11×200×542. F = 6.67×10−916≈4.17×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.2 × 10⁻¹⁰ N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
U = −GMEr. U = −6.67×10−11×6×10244.48×107. U = −8.936×106J/kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -8.9 × 10⁶ J/kg. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
Force between two masses: F = Gm2r2 = 6.67×10−116×652 = 9.61×10−11N. Two forces at 60°: FR = F2+F2+2F2cos60∘. FR = (9.61×10−11)2(1+1+1) = 9.61×10−113. FR≈1.66×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.7 × 10⁻¹⁰ N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ΔE = −GMEm(1r2−1r1). r1 = 3.84×107m, r2 = 7.68×107m. ΔE = −6.67×10−11×6×1024×200(17.68×107−13.84×107). ΔE = −8.004×1016(−1.302×10−8)≈1.04×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.0 × 10⁹ J. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
3 pairs: V = −3Gm2r. V = −36.67×10−11×5×54. V = −3×4.169×10−11 = −1.25×10−10J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -1.2 × 10⁻¹⁰ J. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
g(d) = g0(1−d/RE). 6.86 = 9.8(1−d/RE). 1−d/RE = 0.7. d/RE = 0.3. d = 0.3×6.4×106 = 1.92×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.9 × 10⁶ m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ΔE = −GMEm(1r2−1r1). r1 = 5.12×107m, r2 = 1.024×108m. ΔE = −6.67×10−11×6×1024×400(11.024×108−15.12×107). ΔE = −1.601×1017(−9.766×10−9)≈1.56×109J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.6 × 10⁹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
g(h) = g(1+h/RE)2. h = RE/6, 1+h/RE = 1+1/6 = 7/6. g(h) = 9.8(7/6)2 = 9.8×3649 = 7.2m/s2. Mass: m = 392/9.8 = 40kg. Weight: W = 40×7.2 = 288N.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
ve = 2GMR decreases with altitude as R+h increases, making option 4 correct. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It decreases with altitude. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
T2 = 4π2GMEr3 for satellites, where k = 4π2GME. Thus, k depends on the mass of the central body (Earth) and universal constants, not the satellite’s mass. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Mass of the central body. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
