Assume the earth is a uniform sphere of mass M and radius R. As strange as it may sound, if one can dig a long tunnel from one side of the Earth straight through the center and exit the other end, any object falling into the tunnel will appear at the other end (i.e. the opposite side of the Earth) in just 2530 s (42.2 min). Call that time t. Let t be a function of G, M, and R, where G = 6.67 x 10^-11 m3 kg−1 s−2 is the Universal Gravitational Constant, M = 5.98 x 10^24 kg, and R = 6400 km. (a) From dimensional analysis alone find the expression for t, up to a numerical constant c. (b) Determine the value of c by using the above values in the expression found in part (a)

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A: The vector equation is : r (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^, t∈[0;2π]   The tangent…

Q: velocity of the proton in units of km/s

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Q: A planet of mass 5 ⨯ 1024 kg is at location m. A star of mass 4 ⨯ 1030 kg is at location m. It will…

A: The position of the planet and star is drawn below:

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A:

Q: Assume that planet A has radius RA and mass MA, and planet B has radius Rg and mass Mg. Let gA and…

A: radius of planet A=RAmass of planet A=MAradius of planet B=RBmass of planet B=MB

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Q: you are asked to verify Kepler's Laws of Planetary Motion. For these exercises, assume that each…

A: Solution:

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A: The force due to first sphere is, The force due to second sphere is,

Q: Determine the exact gravity force on B due to P. (

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Q: A 4.4 kg mass weighs 35.64 N on the surface of a planet similar to Earth. The radius of this planet…

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A: Given: The radius of the earth is re = 6400 km

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Q: Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean, you…

A: Based on the given information in the question , the following diagramcan be drawn .

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Q: The value of g at any latitude o may be obtained from the formula g = 32.09(1+ 0.0053 sin' 4) ft/s…

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Q: In the x-y plane there is an infinitely thin layer of uniform density Y2(unit: kg/m²), and on the…

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Q: There is a circle centered at the origin of a coordinate system S with radius R. Consider a…

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A: Given data: Radius of the ring, R=6.5 m Mass density of first and third quadrant of the ring, ρ1=3.6…

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A: Given quantities: mass of the passenger (m) = 82 kg height through which it descends (H) = 391 m…

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A: The space shuttle orbits 271 km above the earth

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A: radius of planet A=RAmass of planet A=MAradius of planet B=RBmass of planet B=MB

Q: While visiting Planet Physics, you toss a rock straight up at 11 m/s and catch it 2.5 s later. Your…

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Q: Two particles move about each other in circular orbits under the influence of gravitational forces,…

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Q: Four planets of equal mass m are rotating with speed v in a circular orbit of radius R. The four…

A: Gravitational force is given as F = Gm1m2/r2

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Q: it of the moon about the earth is approximately circular, with a mean radius of 3.84 x 10% m. It…

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A: Given: Mass of planet is 5.97 x 1024 kg. Mass of star is 1.99 x 1030 kg. Distance during perihelion…

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Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.