Derive the expression a=mgr/I +mr^2 for the acceleration a = ar of the falling mass m "
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"Derive the expression a=mgr/I +mr^2 for the acceleration a = ar of the falling mass m "
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- The gravitational constant G was first measured accurately by Henry Cavendish in 1798. He used an exquisitely sensitive balance to measure the force between two lead spheres whose centers were 0.27 mm\ apart. One of the spheres had a mass of 168 kg, while the mass of the other sphere was 0.73 kg. What was the ratio of the gravitational force between these spheres to the weight of the lighter sphere?Please solveWhat is the ratio of the sun's gravitational pull on Mercury to the sunfs gravitational pul on the earth? The radius of the orbit of Mercury is RM 5.79 x 10 m and its mass is my - 1.50 × 10 m and its mass is mp = 5,97 x 10 kg 5.97 x 1024 kg =D3.30x10 kg. The radius of the orbit of Earth is Rp 阳 AX中 FM FE
- Part 2 (b) What initial speed is needed so that when the object is far from Saturn its final speed is 0 m/s? (This is called the "escape speed.") Vescape = i m/sAn object of mass is released from rest a distance 3.2R above the surface of a planet, which has no atmosphere, of mass and radius . It strikes the surface of the planet with a speed given by v=c (sqt GM/R) , where c is a constant What is the numerical value of ?a)Find the magnitude of the gravitational force (in N) between a planet with mass 6.75 ✕ 1024 kg and its moon, with mass 2.65 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m. (answer in N) (b)What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.)(answer in m/s2) (c)What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.)(answer in m/s2)
- The radius Rhand mass Mh of a black hole are related by R₁ = 2GM₁/c², where c is the speed of light. Assume that the gravitational acceleration as of an object at a distance r= 1.001Rh from the center of a black hole is given by ag = GM/r² (it is, for large black holes). (a) In terms of Mh, find ag at ro. (b) Does sag at ro increase or decrease as M₁ increases? (c) What is ag at ro for a very large black hole whose mass is 1.54 × 10¹3 times the solar mass of 1.99 × 10³⁰ kg? (d) If an astronaut with a height of 1.66 m is at råwith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet? (e) Is the tendency to stretch the astronaut severe?The mean diameters of X and Y, two planets in the same solar system, are 6.5 x 10³ km and 1.2 x 104 km, respectively. The mass of x is 0.21 times the mass of Y. The value of g on Y is 8.1 m/s². (a) What is the ratio of the mean density of X to that of Y (Px / Py)? (b) What is the value of g on X? m/s² (c) The mass of Y is 4.372 x 1024 kg. What is the escape speed on X? m/sA mass ?m is suspended from a massless spring of natural length 90 cm with the spring constant ?=10k=10 Nm-1 and causes the spring to extend by 9.5 cm. Assuming the gravitational field strength ?=9.8g=9.8 ms-2, calculate the value of the mass on the spring. Give your answer in SI units