āĻĒৃāĻĨিāĻŦীāϰ āĻāύāϤ্āĻŦ āĻŦāϰ্āϤāĻŽাāύ āĻāύāϤ্āĻŦেāϰ 4 āĻুāύ āĻ āĻŦ্āϝাāϏাāϰ্āϧ āĻŦāϰ্āϤāĻŽাāύ āĻŦ্āϝাāϏাāϰ্āϧেāϰ āĻ āϰ্āϧেāĻ āĻšāϞে āĻāĻŽাāĻĻেāϰ āĻāĻāύেāϰ āĻি āĻĒāϰিāĻŦāϰ্āϤāύ āĻšāĻŦে ?
āĻāĻāύেāϰ āĻĢāϰ্āĻŽুāϞা: F = G M m R 2 F = \frac{G M m}{R^2} āĻāĻাāύে: F F āĻšāĻ্āĻে āĻāĻāύ (gravitational force), G G āĻšāĻ্āĻে āĻুāϰāϤ্āĻŦāĻāύিāϤ āϧ্āϰুāĻŦāĻ, M M āĻšāĻ্āĻে āĻĒৃāĻĨিāĻŦীāϰ āĻāϰ, m m āĻšāĻ্āĻে āĻŦāϏ্āϤুāĻিāϰ āĻāϰ, R R āĻšāĻ্āĻে āĻĒৃāĻĨিāĻŦীāϰ āĻŦ্āϝাāϏাāϰ্āϧ। ā§§. āĻāϰেāϰ āĻĒāϰিāĻŦāϰ্āϤāύ: āĻĒৃāĻĨিāĻŦীāϰ āĻāύāϤ্āĻŦ Ī \rho āĻĻ্āĻŦাāϰা āĻĒৃāĻĨিāĻŦীāϰ āĻāϰ M M āĻāĻŦং āĻŦ্āϝাāϏাāϰ্āϧ R R āĻāϰ āĻŽāϧ্āϝে āϏāĻŽ্āĻĒāϰ্āĻ āϰā§েāĻে। āĻāύāϤ্āĻŦেāϰ āϏāĻ্āĻে āĻāϰ āĻ āĻŦ্āϝাāϏাāϰ্āϧেāϰ āϏāĻŽ্āĻĒāϰ্āĻেāϰ āĻĢāϰ্āĻŽুāϞা: M ∝ Ī R 3 M \propto \rho R^3 āĻāĻāύ, āĻĒৃāĻĨিāĻŦীāϰ āĻāύāϤ্āĻŦ ā§Ē āĻুāĻŖ āĻāĻŦং āĻŦ্āϝাāϏাāϰ্āϧ āĻ
āϰ্āϧেāĻ āĻšāϞে: āύāϤুāύ āĻĒৃāĻĨিāĻŦীāϰ āĻāύāϤ্āĻŦ āĻšāĻŦে 4 Ī 4\rho , āύāϤুāύ āĻĒৃāĻĨিāĻŦীāϰ āĻŦ্āϝাāϏাāϰ্āϧ āĻšāĻŦে R 2 \frac{R}{2} āϤাāĻšāϞে āύāϤুāύ āĻāϰ āĻšāĻŦে: M ′ ∝ ( 4 Ī ) ( R 2 ) 3 = 4 Ī ⋅ R 3 8 = 1 2 Ī R 3 M' \propto (4 \rho) \left( \frac{R}{2} \right)^3 = 4 \rho \cdot \frac{R^3}{8} = \frac{1}{2} \rho R^3 āĻ
āϰ্āĻĨাā§, āύāϤুāύ āĻĒৃāĻĨিāĻŦীāϰ āĻāϰ āĻšāĻŦে āĻŦāϰ্āϤāĻŽাāύ āĻĒৃāĻĨিāĻŦীāϰ āĻāϰেāϰ āĻ
āϰ্āϧেāĻ। ⧍. āĻুāϰāϤ্āĻŦāĻāύিāϤ āĻাāύেāϰ āĻĒāϰিāĻŦāϰ্āϤāύ: āĻুāϰāϤ্āĻŦāĻāύিāϤ āĻাāύ āĻŦা āĻāĻāύেāϰ āĻĢāϰ্āĻŽুāϞাā§ āĻĒৃāĻĨিāĻŦীāϰ āĻāϰ āĻāĻŦং āĻŦ্āϝাāϏাāϰ্āϧেāϰ āĻĒāϰিāĻŦāϰ্āϤāύ āĻšিāϏাāĻŦ āĻāϰāϞে: F ′ = G M ′ m R ′ 2 F' = \frac{G M' m}{R'^2} āĻāĻাāύে M ′ M' āĻšāĻ্āĻে āύāϤুāύ āĻĒৃāĻĨিāĻŦীāϰ āĻāϰ āĻāĻŦং R ′ R' āĻšāĻ্āĻে...
Comments
Post a Comment