#equilateral triangle problem

Work, Energy and Orbital Mechanics

Three masses of 18kg each form an equilateral triangle with side 12m. What is the net force on one mass? (G\=6.67×10−11N

Force between two masses: F = Gm2r2 = 6.67×10−1118×18122 = 1.50×10−10N. Two forces at 60°: FR = F2+F2+2F2cos⁡60∘. FR = (1.50×10−10)2(1+1+1) = 1.50×10−103. FR≈2.60×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.6 × 10⁻¹⁰ N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Potential Energy of Mass Systems

Three 5kg masses form an equilateral triangle of side 4m. What is the potential energy of the system? (G\=6.67×10−11N m2

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.

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Gravitational Potential and Field

Three masses of 10kg each form an equilateral triangle with side 7m. What is the net force on one mass? (G\=6.67×10−11N

Force between two masses: F = Gm2r2 = 6.67×10−1110×1072 = 1.36×10−10N. Two forces at 60°: FR = F2+F2+2F2cos⁡60∘. FR = (1.36×10−10)2(1+1+1) = 1.36×10−103. FR≈2.36×10−10N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.4 × 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.

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Gravitational Potential and Field

Three 6kg masses form an equilateral triangle of side 8m. What is the potential energy of the system? (G\=6.67×10−11N m2

3 pairs: V = −3Gm2r. V = −36.67×10−11×6×68. V = −3×3.0015×10−11 = −9.0×10−11J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -9.0 × 10⁻¹¹ J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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