A uniform distribution of dust in the solar system adds to the gravitational attraction of the Sun on a planet an additional force F = −m C r where m is the mass of the planet, C is a constant proportional to the gravitational constant and the density of the dust, and r is the radius vector from the Sun to the planet (both considered as points). This additional force is very small compared to the direct Sun-planet gravitational force. Calculate the period of radial oscillations for slight disturbances from this circular orbit.

Q: A pendulum makes 10 swings every 15 seconds on Earth. You take the same pendulum to the surface of a…

A: as per our guidelines we are supposed to answer only one question. Kindly repost other questions as…

Q: A spring hangs vertically with one end attached to a suspension point. A mass of 0.68 kg is attached…

A: Mass attached= 0.68Kg Spring Constant, k=128 N/m     OBJECTIVE- To find frequency of mass+spring…

Q: A Ferris wheel is 27 meters in diameter and completes 1 full revolution in 12 minutes. revolves…

A: Diameter, d = 27 m Radius, r = d/2 = 13.5 m One revolution in 12 minutes.  Distance of ferris wheel…

Q: A tall building is swaying back and forth on a gusty day. The wind picks up and double the amplitude…

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Q: Problem 6: A uniform rod of mass M and length L is free to swing back and forth by pivoting a…

A: Hi i have solved all the three parts .

Q: Geologists use pendulums to find tiny differences in the earths gravitational field from one…

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Q: 10° kg m-3 with radius Rp = 3.9 × 103 km, while period of the Calculate the period of oscillation of…

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Q: How will the period of an oscillating system change if its angular frequency is increased by a…

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Q: A particle of mass m is dropped in a tunnel through the earth (of mass M and radius R). Find its…

A: (given) m is the mass of a particle, M is the mass of the earth, R is the radius of the earth, d is…

Q: Example -mass = 300kg 15 oscillations= 21 seconds  Displacement = 50 cm A) mass = ? 15…

A: the spring constant can be calculated using the example.

Q: A small ball is attached to one end of a spring that has an unstrained length of 0.193 m. The spring…

A: Unstrained length L =0.193 m   Stretch in first case x1=0.0176 m   Velocity v=3.98 m/s  Lets take…

Q: A 10-kg block is attached to a very light horizontal spring on a smooth horizontal table. A force of…

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Q: Objective:  Measure the gravitational field  g  using the period of a simple pendulum I need to…

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Q: a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a…

A: It is given that,

Q: You are riding on a Ferris Wheel that rotates 1 revolution every 30 seconds. It has a diameter of 17…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 53.0…

A: T= 2πlgT is time periodl is length of pendulumg is gravitational accelerationHere  90 full swing in…

Q: Which is the right way to displace the bob for oscillations to measure the time? II. III. I. 0> 40°I…

A: To measure the oscillation of bob, the string of the bob should not be loose. When string is loose…

Q: planet (see Figure). A mass 3.80 kg is secured to the end of a chord (see Figure) of length 7 m. The…

A: Given  Mass of planet = M = 102.413*10²⁴ kg Radius of planet=R =24764 km  Mass of pendulum = m =3.80…

Q: The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a…

A: The period of simple pendulum is found as, T=Time takenNumber of oscillations=218 s109=2 s The…

Q: 20. A student from Planet X was performing an experiment about simple pendulum to determine its g…

A: The m=20cycle  Time t=8sec Length of the string L=0.2m

Q: 2) A 1.10-kg mass oscillates according to the equation x=0.660 cos7.30t where x is in meters and t…

A: Mass of the object is M= 1.10 kg

Q: particle of mass m hangs from a light spring inside a lift (see figure). When the lift is at rest,…

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Q: [h!] A conical pendulum consists of a weight (or bob) fixed on the end of a string or rod suspended…

A: The time taken by the bob to complete one horizontal circle is called the time period of the conical…

Q: A peg on a turntable moves with a constant tangential speed of 0.61 m/s in a circle of radius 0.22…

A: The motion of shadow represents a simple harmonic motion

Q: Two pendula are shown in the figure. Each consists of a solid ball with uniform density and has a…

A: Given that----- Radius L = 1.3 m. Question ❓ a) Find the period T of the left pendulum for small…

Q: A small ball is attached to one end of a spring that has an unstrained length of 0.212 m. The spring…

A: Given:speed ,v=2.88 m/sradius,r=0.212m+0.0160m               =0.2281 m stretch,x= 0.0160 mNow,The…

Q: A spring is compressed by 0.0857 m and is used to launch an object horizontally with a speed of 2.44…

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Q: Two pendula are shown in the figure. Each consists of a solid ball with uniform density and has a…

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Q: A simple pendulum that has a period T on Earth’s surface is transported to the surface of a planet…

A: SOlution:

Q: A broken clock is a cylinder of constant density with a 15 cm radius. I hangs from a nail 1 cm above…

A: Given: The position of the nail from the center of cylinder is 1 cm. The radius of the cylinder is…

Q: After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0…

A: Write the given values with the suitable variables. l=46 cm=0.46 mn=98t=145 s Here, l is the length,…

Q: A ball is attached to a string of length 4 m to make a pendulum. The pendulum is placed at a…

A: Length of the pendulum, L = 4 m  height, h = radius of earth Radius of earth, R = 6400 km

Q: After a long space trip where you are in stasis, your autonomous ship lands you on a planet you…

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Q: A 500-g object connected to a light spring with a spring constant of 10.0 N/m sits on a frictionless…

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Q: wo pendulums have the same dimensions (length L) and total mass (m). Pendulum A is a very small ball…

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Q: While at dinner, you notice a chandelier that looks like a simple pendulum swinging back and forth…

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Q: While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which…

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Q: A conical pendulum has length l and the angle made by the string with vertical is 0 = 38° . The mass…

A: The time period of a conical pendulum is given by:T=2πLcosθg......(1)where,T is the period of…

Q: A canonical pendulum is a mass on the end of a cord, where the mass moves at a constant speed in a…

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Q: A ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meter above the…

A: The minimum height is given as 1 meter above the ground level, and the diameter of the wheel is…

Q: A small ball of mass m is suspended from a string of length L. The ball revolves with constant speed…

A: Given,

Q: MärkxsfH) Problem 1: A mass of 20 grams stretches a spring by 10/169 meters. (a) Find the spring…

A: The given values are,