List of top Physics Questions on Centripetal forces asked in JEE Advanced

A particle of mass 𝑚 is under the influence of the gravitational field of a body of mass 𝑀 (≫ 𝑚). The particle is moving in a circular orbit of radius \(𝑟_0\) with time period \(𝑇_0\) around the mass 𝑀. Then, the particle is subjected to an additional central force, corresponding to the potential energy 𝑉c(𝑟) = 𝑚𝛼/𝑟 3 , where 𝛼 is a positive constant of suitable dimensions and 𝑟 is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius\( 𝑟_0\) in the combined gravitational potential due to 𝑀 and 𝑉c(𝑟), but with a new time period \(𝑇_1\), then\( (𝑇_1^2  − 𝑇_0^ 2 )/𝑇_1^ 2\) is given by [𝐺 is the gravitational constant.]

A particle of mass m is moving in a circular orbit under the influence of the central force\( f(r) = −kr\), corresponding to the potential energy \(v(r) = \frac{kr^2}{2}\), where \(k\) is a positive force constant and \( r\) is the radial distance from the origin. According to the Bohr’s quantization rule, the angular momentum of the particle is given by \(L= nℏ\), where\( ℏ = ℎ/(2pi), ℎ\) is the Planck’s constant, and \(n\) a positive integer. If \(v\) and \(E\) are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

Suppose the gravitational force varies inversely as the nth power of distance. Then, the time period of a planet in circular orbit of radius R around the sun will be proportional to